A makeshift market outside a mosque in Istanbul.   (Photo: Allison Maletz)

Hollywood
Two nights + weird magic + morning chilaquiles = $357 for a two-nighter.
There are two L.A.’s: the glitzy-glammy one and the kitschy-trashy one. Only the latter—centered on eternally seedy Hollywood—qualifies as both fun and cheap to visit. Base yourself at the Magic Castle Hotel, part of a private magician’s clubhouse that lets guests crash nightly magic shows (from $164, shows from $20; magiccastlehotel.com). Everything else you need is right on Hollywood Boulevard. For breakfast, eat Mexico City–caliber chilaquiles at the new Lotería Grill ($9; loteriagrill.com). Watch cutting-edge video art at the LACE center (artleak.org). Catch a Disney movie in 3-D, sometimes preceded by a floor show and the dropping of confetti, at El Capitan Theater (818-845-3110). If you must leave the boulevard, a $1.35 Metro ride gets you to the architecturally stunning Walt Disney Concert Hall, where legendary conductor Esa-Pekka Salonen is wrapping up his final season with the L.A. Philharmonic (go to laphil.com for a schedule). Splurge a little on drinks at Amanda Demme’s latest hot spot, the Stork (323-462-3663).

Istanbul, Turkey
Seven nights + ottoman China + rooftop tea = $1363 for a week.
In Istanbul, Europe meets Asia, ancient meets modern, and expensive, happily, meets cheap. For a quick introduction, catch a tram and circle the Eminonu historic district, passing the Grand Bazaar, Galata Bridge, and the Istanbul Modern Museum. If saving money is your main concern, explore artsy Cukurcuma, bustling with antique stores, nightclubs along Algeria Street, and dozens of boutiques. Snatch up some eighties-ish off-the-shoulder T-shirts or salwars at Kop-Art, a shop–cum–art space (kop-art.com). Grab some Ottoman-era ceramic dishes for about $100 at Anadol Antik (90-212-251-5228). Take tea ($2.50) at 5.Kat’s rooftop tables on the Bosphorus (5kat.com). Stay at the accurately named Lush Hotel (from $180; lushhiphotel.com).