Endless rooms, river views: Rockefeller State Park Preserve in Tarrytown.

5. TARRYTOWN

Stop a random local in Tarrytown and ask for directions to “the Rockefeller estate,” and you’re likely to be pointed to Kykuit. Spectacular as that property is with its lush gardens, Calder and Moore sculptures, and Picasso tapestries, what you really want to find is the Rockefeller State Park Preserve. John D. Sr., the Standard Oil baron, began acquiring Dutch farmland here in the 1890s, and in this instance, he was a very aggressive force for exploiting nature for nature’s sake. The preserve now comprises 1,200 acres of richly varied terrain. One of the prime attractions is hiking, in part because you choose the degree of difficulty: flat ground past open fields of roaming cattle, gently sloping hills leading up to a spectacular overlook of the Hudson River, steeper ups and downs through dense woods to gaze at one of the state’s largest bluebird populations.The preserve is open year-round, the hiking trails becoming ideal cross-country-skiing trails each winter. The mostly shallow Pocantico River has a few small rapids and recreational fishing holes, and all of its banks are well suited to picnicking. Opening this fall adjacent to the preserve: the Stone Barns Center for Food and Agriculture, an educational center, and a restaurant called Blue Hill at Stone Barns, run by the owners of Blue Hill in Greenwich Village, which will serve organic food grown at the preserve. And don’t miss the Union Church of Pocantico Hills, in the tiny hamlet of Sleepy Hollow, with its refulgent stained-glass windows by Marc Chagall and rose window by Henri Matisse.

The preserve has more than scenic significance. It’s said to be the site where characters in “The Legend of Sleepy Hollow” drifted off to slumber from the effects of an Indian spell. Speaking of Washington Irving, Tarrytown runs tours of the Old Dutch Church Burying Ground year-round; at Halloween, there’s “Legend Weekend,” with enough headless horsemen to supply Tim Burton with decades of sequels. When you’ve had your fill of nature and death, head south for a complete change of tone: the three-ring circus known as Stew Leonard’s, equal parts Greenmarket, barbecue pit, petting zoo, and dairy, in nearby Yonkers.

Rockefeller State Park Preserve, Rte. 117, Tarrytown (914-631-1470). Union Church of Pocantico Hills, Rte. 448, Sleepy Hollow (914-631-8200). Friends of the Old Dutch Burying Ground, 430 N. Broadway, Sleepy Hollow (914-631-1123). “Legend Weekend,” Philipsburg Manor (914-631-8200). Stew Leonard’s, 1 Stew Leonard Dr., Yonkers (914-375-4700).

6. THE BRONX

Yes, you could easily assume that the Bronx Zoo, what with the new Siberian-tiger exhibit—where kids come face-to-face with the beautiful beasts through a glass shelter—trumps every other family outing in the northernmost borough. But then you’d miss the New York Botanical Garden. Check out the rain-forest display at the Conservatory, where you’ll undoubtedly get shpritzed here and there. The Everett Children’s Adventure Garden runs ongoing nature labs to examine plants and insects. Or travel to the Bronx’s Gold Coast along the Hudson, where there’s always something going on at beautiful Wave Hill, the 28-acre garden that was once home to Teddy Roosevelt, Mark Twain, and conductor Arturo Toscanini. Craft workshops are environmentally oriented, and the Barefoot Dancing sessions on lush lawns are a showcase for world music. Cross the borough for dinner in the quiet village of City Island. The 20-year-old Portofino Restaurant has developed a buzz since new owners took over recently. The northern Italian cuisine includes a handful of daily fish specials. As for kids, a co-owner says, “there’s no such thing as ‘we don’t have it.’ ” The kitchen will adjust anything from the menu to make a kid-friendly meal, including restyling chicken parmigiana into chicken fingers.

For dessert, head over to Lickety Split, the ice-cream parlor that’s a local favorite.

Bronx Zoo, Fordham Rd. and Bronx River Pkwy. (718-367-1010). New York Botanical Garden, Bronx River Pkwy. (Exit 7W) and Fordham Rd. (718-817-8700). Wave Hill, 675 W. 249nd St., at Independence Ave. (718-549-3200). Portofino, 555 City Island Ave. (718-885-1220; portofinocityisland.com). Lickety Split, 295 City Island Ave. (718-885-9195).

7. NEW JERSEY

It almost looks like a mosque from the Jersey Turnpike. Liberty Science Center, directly across the harbor from the Battery, houses exhibits that New York museums pass up or miss altogether. Now on view, for example, is “Bones,” a show in which kids try on casts and learn how to stay strong. The Invention Floor is for the engineer in every child. In the domed six-story-high Imax theater, see Jane Goodall’s Wild Chimpanzees, depicting her simian behavior research in Africa. Picnic on the grounds at Liberty State Park, then head a few minutes away to New Jersey Performing Arts Center for its family series, which this coming season includes Théātre Sans Fil from Quebec doing Hansel and Gretel with puppets and special effects. Also on tap is the dramatic musical Laura Ingalls Wilder: Growing Up on the Prairie. For dinner, a popular stop for families is Seabra’s Rodizio. Kids will love the handheld wooden cylinder that they control to tell the wait staff they want more (the green side) or they’ve had enough (the red side). There are plenty of exotic dishes for grown-ups—buffalo, ostrich, and alligator—but the kids will be just as happy with the ribs, filet mignon, and fries. For dessert, try the Portuguese caramel meringue cake.

Liberty Science Center, Liberty State Park, 251 Phillip St., Jersey City (201-200-1000; lsc.org). New Jersey Performing Arts Center, 1 Center St., Newark (1-888-GO-NJPAC; njpac.org). Seabra’s Rodizio, 1034 McCarter Highway, Newark (973-622-6221).

8. CONNECTICUT

Coney Island has the history, both glittering and tawdry, and the rides, but if it’s an efficient, clean, multifaceted amusement park that you want—one that combines rural charms with its scream-inducing roller coasters—then head slightly north. Connecticut’s Lake Compounce, between Bristol and Southington, has been a family destination since before the Civil War. Much has changed since “the southern method of cooking lamb” was one of the park’s main attractions. But catered lakeside picnics are still welcome, and the water itself remains pristine, perfect for swimming, gazing at from the sand beach, or cruising across at a leisurely pace aboard the Mark Twain, a vintage sternwheeler. The amusement park offers two classic wooden roller coasters: the Wildcat, built in 1927, and the Boulder Dash—the only roller coaster in the world to be built into the side of a mountain, which is all the more amazing when you’re whizzing past granite and trees at 65 miles per hour. The throwback feeling is complete with spins on the 120-foot Ferris wheel or the bumper cars and a trip through Ghost Hunt, a haunted house with the added thrill of being able to “shoot” the ghosts.

Spirits of a different sort are plentiful all over the Nutmeg State: Connecticut offers the railroad hobbyist, or just the kid who loves a cool train, nearly a dozen choices of places to see restored reefers, sleepers, and boxcars. The Railroad Museum of New England, in Naugatuck, offers fascinating stationary exhibits of everything from cabooses to signal towers, and each summer, there’s an inevitable visit from a certain blue British locomotive named Thomas. The true highlight, though, is the eighteen-mile round-trip train ride inside beautifully restored 50-year-old passenger cars. The trip through Litchfield Hills and Mattatuck State Forest and over the Naugatuck River is especially pretty in the fall.

About 45 minutes south, in East Haven, is the Shore Line Trolley Museum, the oldest operating trolley museum in the United States. There are nearly 100 cars in the collection, most of them dating to the heyday of trolley travel in the Northeast, from 1900 to 1930, and many of them marvels of rattan seating and varnished hardwood detail. A trolley trip inside one of these gleaming beauties runs three miles along the original tracks of a scenic country line that has been in continuous operation since July 31, 1900. The Yale University campus in New Haven offers plenty of other things to do as well: With teens, stroll the Yale Art Gallery, whose landmark Louis I. Kahn building is undergoing a remarkable renovation, or take in a show at Yale Repertory Theatre to catch a glimpse of future Streeps, Turturros, and Winklers. New Haven also offers a wealth of kid-friendly food served in historic locations. Louis’ Lunch is allegedly the first restaurant to ever put a grilled hamburger between two slices of bread, in 1895. Archie Moore’s Bar & Restaurant features chicken wings and apple crisps. There’s also Naples Pizza, where the menu includes a satisfying spaghetti and meatballs, as well as the slices that have nourished four generations of Elis.

Lake Compounce Theme Park, Rte. 229, Southington (860-583-3300). The Railroad Museum of New England, Thomaston (860-283-7245); Naugatuck Railroad (203-575-1931; www.rmne.org). The Shore Line Trolley Museum, 17 River St., East Haven (203-467-6927). Yale University Art Gallery, 1111 Chapel St., New Haven (203-432-0600; www.yale.edu/artgallery). Yale Repertory Theatre, 1120 Chapel St., New Haven (203-432-1234; yalerep@yale.edu).

Just add water: Sliding away at Splish Splash in Riverhead.

9. RIVERHEAD

It’s nearly impossible to think of another small city that’s home to such disparate attractions. There’s the region’s best NASCAR short-track competition at Riverhead Raceway. The drivers are dentists, truckers, and students during the week—which may be why they run as hard as Tony Stewart on the quarter-mile banked oval each weekend. Every schoolkid will delight in Riverhead Raceway’s full-size school-bus demolition derbies. And want your teenager to put down the PlayStation? Tell him he can participate in the raceway’s spectator drag-racing night.

Of course, that depends on whether he has any adrenaline left after plunging down the 70-degree, 80-foot-long Cliff Diver water slide at Splish Splash water park. Or through the Abyss, or Shotgun Falls, or any of the other two-dozen wet adventures. Splish Splash is a kitschy 36-acre collection of watery wonders both wild and gentle, including a giant plastic elephant spouting cool sprays and a kiddie pool with a pirate ship.

For a very different aquatic experience, head over to the Riverhead Foundation for Marine Research and Preservation. Next to the Atlantis Marine World Aquarium, the foundation is the only authorized rescue facility in New York State for stranded marine mammals and sea turtles. The rehabilitating creatures are on display while awaiting their return to open waters. Seal-observation cruises in Hempstead Bay are available December through mid-April; ecologists are onboard to explain the habitats we too often take for granted.

Riverhead also has the great outdoors: Once you’ve had enough of the Peconic River, the Tanger Factory Outlet Center awaits, with its 170 stores—from Liz Claiborne to Reebok, from Oshkosh B’gosh to Publishers Warehouse. Escape the mall for dinner, though; for a sense of history, and locally grown corn in season, try Tweed’s Restaurant & Buffalo Bar, in the beautifully restored turn-of-the-twentieth-century J. J. Sullivan Hotel. Though if the animal rescuer is with you, maybe not: The huge stuffed head of the last bison shot by Teddy Roosevelt is mounted on the dining-room wall.

Riverhead Raceway, Route 58 (631-842-7223). Splish Splash, 2549 Splish Splash Dr. (631-727-3600). Riverhead Foundation for Marine Research and Preservation, 467 E. Main St. (631-369-9840). Tanger Factory Outlet Center, 1770 West Maine St., Ste. 200 (800-407-4894; 631-369-2732). Tweed’s Restaurant & Buffalo Bar, J.J. Sullivan Hotel, 17 E. Main St. (631-208-3151).