By train: Philadelphia, Pennsylvania (2 hours from NYC)
Part of the College of Physicians of Philadelphia, the unforgettable and disturbing Mtter Museum(19 S 22nd St; 215-563-3737, collegeofphysicians.org; $14) has more than 20,000 anatomical and medical oddities on display, dating back to the 19th century—including a plaster cast of conjoined twins, a stretched-out colon more than eight feet long and the well-preserved Soap Lady, a woman whose body fat turned to a soaplike wax after burial. Following that, the Mummers Museum(1100 S 2nd St; 215-336-3050, mummersmuseum.com; $3.50) may seem almost tame in comparison—the institution showcases string music and extravagant costumes from the city's 10,000-strong annual New Year's parade. "Mummers are working people who, once a year, put on incredible outfits," explains the museum's executive director, Palma Lucas. "Some with hundreds of mirrors on them, sequins and headdresses."
Philly is filled with public art, but none is as exuberant as Philadelphia's Magic Gardens(1020 South St; 215-733-0390, philadelphiasmagicgardens.org; $4), a labyrinthine mosaic installation that artist Isaiah Zagar fashioned on a formerly vacant lot. The Gardens' winding tunnels and sculptures are covered in found objects like bicycle wheels, mirror shards and hand-painted tiles, glittering a half-block long. By the time you get through that, you'll have earned yourself a hearty meal at Carman's Country Kitchen(1301 S 11th St, 215-339-9613), which prides itself on putting "the cunt back in country." The four-item menu changes every day, and brunch is served daily—last week featured pancakes and waffles with bourbon banana sauce, and cracker-coated catfish (each $12). Munch while admiring the restaurant's considerable collection of phallic ornaments.
Since everything else you set eyes on in Philly will be completely bizarre, rest your head at the convenient and elegant bed-and-breakfast La Reserve(1804 Pine St between 18th and 19th Sts; 215-735-1137, lareservebandb.com).
By plane: Charleston, South Carolina (2 hours from NYC)
Charleston is known for being picturesque, but quirky details abound. Poke your head into the Waring Library's Macaulay Museum of Dental History(175 Ashley Ave; 843-792-2288, waring.library.musc.edu) to see curiosities such as a re-creation of a 1905 dentist's office, plus some frightening dental instruments. The 153-acre Magnolia Cemetery(70 Cunnington St, 843-722-8638), located on the mossy banks of the Cooper River four miles outside the center of town, dates to before the Civil War. Situated among the 33,000 graves of politicians, bootleggers and madams is a pyramid mausoleum and a baby-carriage-shaped tombstone. "One tombstone just says BE CAREFUL," notes superintendent Beverly Donald. Considering that alligators and hawks roam the property, that's advice worth heeding. The trek to Charleston's barrier isle Johns Island is worth it, if only to take in the sight of the thick, twisted limbs of the approximately 400-year-old Angel Oak Tree(Angel Oak Park, 3688 Angel Oak Rd; 843-559-3496). "Large trees are a real gathering place in the South," says park manager Mary Richardson. "They're a part of our lives." Good restaurants are also gathering spots. For classic local flavor, order a bottomless plate of steamed fresh oysters ($23.50) at Bowens Island Restaurant(1870 Bowens Island Rd; 843-795-2757, bowensislandrestaurant.com), where you'll sit on mismatched furniture and gape at the graffiti all over the walls.
The rocking chairs on the porch of the charming Notso Hostel(156 Spring St; 843-722-8383, notsohostel.com) make for a welcoming view after a day full of strange sights.
By car: Newport, Rhode Island (3 hours from NYC)
Newport isn't just about enormous old mansions and preppy people piloting yachts—it's about the strange details that make New England weird and wonderful. Prepare to experience the oddities by grabbing a coconut mojito served with edible baby coconuts ($8) at Salvation Cafe(140 Broadway; 401-847-2620, salvationcafe.com). "I bought almost all of the decor at the Salvation Army next door," says owner Susan LaMond of the space, which resembles a cross between a thrift store and a retro diner, and features two indoor and two outdoor rooms—one of which is a tiki bar that's now open for the season. Take a picture in front of the huge Gulf sign hanging on one of the walls before hitting Touro Park(Mill St off Bellevue Ave) to visit the mysterious Newport Tower. Nobody knows exactly who built it, or when: Some residents have advanced the theory that the round stone-and-mortar structure was fashioned by the Vikings; others think that it was a colonial windmill. Consider its possible origins on a detour drive to nearby Portsmouth, where you can wander among the grave sites of privileged pooches at the K9 Instincts Kennel pet cemetery(837 Wapping Rd, 401-847-1655). Keep an eye out for Pookie's headstone: He belonged to the Duke and Duchess of Windsor.
The Rose Island Lighthouse(401-847-4242, roseisland.org; from $165) sits on an island in Narragansett Bay, and it offers simple rooms to adventurous travelers. You'll need to pump water to flush the toilets, but you'll have this entire island to yourself after the lighthouse's museum closes at 4pm. "It's silent, and there are no bugs," says executive director David McCurdy. "It's a real escape from the city: no stereo or TV. People have a blast, just sitting on Adirondack chairs, drinking wine, and watching the boats sail by."