Continue up Ninth Avenue until you hit the Chelsea Market between 15th and 16th Streets. Stop in for a sweet pick-me-up: a decadent Fat Witch brownie or Eleni's cookie or cupcake. Walk north on Ninth Avenue through the neighborhood of Chelsea until you come to 22nd St, where you'll walk one block west to 10th Avenue. Most of Chelsea's art galleries are between 22nd and 25th Sts. and Ninth and 10th Aves.; see chelseaartgalleries.com for the latest exhibitions and receptions.
After you spend the afternoon gallery hopping, backtrack a little to Ninth Ave. and 16th St., where you'll find the Maritime Hotel. If the sun is out, enjoy a cocktail on the roof cabana before heading down the stairs to Matsuri, a massive (and delicious) Japanese restaurant with more than 200 sakes on offer.
If you want to stay in Chelsea post-dinner, catch a world-class modern dance performance at the Joyce Theater (175 Eighth Ave., 212-691-9740) or, from fall through spring, a play at the renowned off-Broadway Atlantic Theater Company (76 Ninth Ave., 212-691-5919), founded by David Mamet and William H. Macy and housed in a former church.
If today is your final day in New York, head to the Upper West Side to visit the always-fascinating American Museum of Natural History. After you tire of butterflies and dinosaurs, walk a few blocks west to Manhattan's famous food emporium, Zabar's (2245 Broadway at 80th St., 212-496-1234) where you can pick up some smoked fish or hand-sliced pastrami and bagels to-go.
(If natural history isn't your thing, visit one of the museums you didn't get to during the rest of your trip – the Neue Galerie can be fun if you're a Klimt fan, while the Cooper-Hewitt Design Museum is a delight for design aficionados.)
Then catch a train or cab down to Washington Square Park, in the heart of Greenwich Village. After snapping a picture by the Washington Square Arch, if the weather's mild find a bench to enjoy your picnic while being entertained by the students, street performers and people from all walks of life who populate the park.
After you're finished people-watching, exit the park on the south side to West 4th Street, where you'll head east. Once you pass 3rd Avenue, you'll be entering the East Village (which runs roughly between 14th Street on the north, Houston Street on the south, Avenue D on the east and 3rd Avenue on the west). Though now chockfull of restaurants and boutiques, the East Village was the New York's center of counterculture not too long ago. You can still get a taste of its quirky side if you head north on 2nd Avenue until you hit St. Mark's Place, where gritty tattoo parlors sit alongside trendy frozen yogurt shops. Continue east on St. Marks until you run into Tompkins Square Park, which used to be known for vagrants and drug-dealers, but is now more frequented for concerts and a popular dog run.
If strolling through the East Village works up an appetite, stop in for an early dinner at Hearth (403 East 12th St., 646-602-1300) – a "New American" restaurant helmed by former restaurateurs from Craft and Gramercy Tavern – or a glass of wine and light fare at their new next-door wine bar, Terroir (413 East 12th St., no phone).