After spending two to three hours browsing the museum of your choice, take a train or cab over to the majestic Grand Central Station. Marvel at the astronomical ceiling and check out the tempting foodstuffs in the Grand Central Market in the basement, where you can either stop for a quick bite or have a more formal sit-down meal in the historic Grand Central Oyster Bar and Restaurant.
After lunch, hop on the 6 subway line directly from Grand Central to the Spring Street station, on the edge of the Soho shopping district. Wander west on Spring, Prince or Broome Streets between Lafayette and Sullivan Streets for scores of trendy boutiques and furniture stores; you can also turn south on Broadway (the Soho street with the largest concentration of chain stores) to check out the downtown branch of Bloomingdale's as well as Pearl River Mart.
When you've had your fill of browsing (or spending!), head south to Broadway and Canal Streets, at the northern entrance to Chinatown. You may be tempted to spend some more (but not much) for knockoff sunglasses or bags. Continue south into the heart of Chinatown's stores selling knickknacks, spices, candy, fish and baked goods. When you start to work up an appetite, stop for dumplings and bbq pork buns at Dim Sum Go Go (5 East Broadway, 212-732-0796). Reservations aren't accepted, so you may have to queue for a table, but the delicious food is worth the wait. Save room for dessert from the family-run Chinatown Ice Cream Factory (65 Bayard St., 212-608-4170), which offers such unusual flavors as almond cookie, durian and taro, as well as old favorites like green tea and, yes, even chocolate and vanilla for purists.
If it's not too late, backtrack north through Chinatown, cross Canal and head up Mulberry Street, where you'll be smack in the middle of Little Italy. Once known for its large Italian population, the neighborhood is now better known for its touristy restaurants, but can still be fun to visit (if you have a high tolerance for crowds and fried foods) during the Feast of San Gennaro festival in September.
If you have 5 or 6 days, take time to check out Manhattan's charming downtown neighborhoods. (The problem is, you may never want to leave.) Also see more of what New York is famous for, music and/or theater.
Start with a cup of coffee or chai from one of the local cafes in New York City's most charming neighborhood, the West Village. Most boutiques won't open till 11 a.m., so take the time to wander throughout the twisty cobblestone streets, admiring the gorgeous brownstones and perhaps wandering over to the Hudson River for a stroll along the water.
After checking out some stores on Bleecker Street (and lining up at Magnolia Bakery for a taste of their buttery cupcakes or addictive banana pudding), head north up Hudson, a charming street of stores, restaurants and residences, until you reach Gansevoort Street, the border of the Meatpacking District. Though this trendy neighborhood is crowded at night, especially on the weekends, lunchtimes are quite a bit calmer. Enjoy the steak frites or tuna Nicoise at French brasserie (and Meatpacking District pioneer) Pastis (9 Ninth St. at Little West 12th, 212-929-4844), where in nice weather you can eat outside and watch the beautiful people pass by.