I agree with S. B and Kaseyirv -
Chelsea market, NYC food walking tours, the Highline. You can start downtown, walk the highline and end up at Chelsea market for lunch.
If you feel like head to the east side, midtown my current favorite manhattan restaurant is Zengo (3rd Ave and 40th Street) - asian / southwest fusion. sounds strange but they have the most awesome tuna wonton taco appetizers. I dream about them. I've never had a bad meal there and I take clients there frequently.
If you want to do upscale Asian go to the China Grill. it hink it's 53rd between 5th & 6th (Ave of the Americas) Avenues. Everything on their menu is amazing.
If you want to walk around and shop for funky stuff the village is a great option, TriBeCa, NoHo, all the small streets north of Canal. If you're going to be in Chinatown check out Pearl River Mart (on Broadway a couple blocks north of Canal Street) for all kinds of interesting imports from China (fabric, lanterns, incense, wind up toys, slippers, home furnishings, tea, etc.)
It's also a lovely time of year to be outside. Central Park is gorgous with all it's flowering trees (the parked was designed by Frederick Law Olmstead a famous landscape designed in the 1850's) and a stroll to the Metropolitan Museum of Art is a great and interesting way to spend the day (lots of street performers in the park when the weather is nice). If you go in the museum there's a lovely resturant called Petrie Garden Cafe - it overlooks the park on one side the European sculpture court on the other side. The food is very good and reasonably priced. There's also a little know roof top cafe - the food is counter service sandwiches, snacks and ice cream - but there's also a bar. It's an amazing place to have a glass of wine at the end of the day and gaze over Central Park and the Manhattan skyline.
My last suggestion - if the weather is nice is to go the cloisters - the northern most tip of Manhattan up on a high hill. It's part of the Metropolitan Museum of Art - it's a collection of various castles, cloisters and reproductions that have been assembled & built. You'd take the subway and then walk through these beautiful gardens up to the castle on the hill. It overlooks the Husdon River, Palisades, George Washington Bridge, etc. It's a sweet day trip at this time of year when the eweather's nice and everything's in bloom.
Have a wonderful time no matter what you do!