5. Greenpoint
N. 14th St./Nassau Ave./McGuiness Blvd. to Newtown Creek, Newtown Creek to East River

Another surprise—and for a surprising reason: Greenpoint has some of the best public schools in the city, achieving high test scores and parent-satisfaction ratings, in spite of (or perhaps because of) its small population. It is slightly cheaper and safer than adjacent Williamsburg and has a respectable number of restaurants and bars. There are downsides: The retail coverage is patchy, there are few parks, and it sits on top of an underground oil spill that is still being cleaned up after 30 years. But as long as you don’t go swimming in Newtown Creek, it’s a vibrant, affordable place to raise a family.

6. Brooklyn Heights
Atlantic Ave. to Old Fulton St., East River to Court St./Cadman Plaza

Though it’s the most expensive neighborhood in the outer boroughs, Brooklyn Heights is arguably still a good deal. Commute times into the densest parts of Manhattan are faster than all but a few neighborhoods on the island itself. Throw in the newly expanded Brooklyn Bridge Park; perhaps the most beautiful homes in the city (the entire neighborhood is a historic district); and safe, clean, tree-lined streets, and it clearly has a lot to offer. What’s missing? The main retail artery, Montague Street, is underwhelming, and there’s little diversity.