Great question! Here are some of my thoughts.

River:

Along the Hudson River, there are several restaurants. On the Upper West Side, the Boat Basin Cafe is typically very lively when the weather is nice. The American fare is nothing special but it serves all the familiar favorites (burgers, etc.).

South Street Seaport is a popular destination for out-of-towners. There's a ton of chain restaurants, many of which have outdoor seating right next to the water.

Bridge:

One of the "classic" activities for Brooklyn Bridge walkers is to get a slice of pizza at Grimaldi's and then hit up the Brooklyn Ice Cream factory.

Central Park:

On the west side, I would recommend getting a to-go dinner from the Time Warner Center. There's a Whole Foods on the bottom floor and on the 3rd floor holds Bouchon Bakery, which has a delicious cashew butter and jelly sandwich (the brioche bread that holds the spreads melts in your mouth). Then, head back outside and sit in the large circle (Columbus Circle). There is plenty of seating and it is right across the street from the park.

Within the park is the Sheep Meadow Cafe at W. 69th. Dinner options include grilled chicken or steak.

Hope you enjoy your trip!