Hey agnes, not sure how far you're looking to walk but I have a few Upper East Side recs for you.
1.) Shake Shack-has a new location at 154 East 86th Street bet. Lexington Ave. & 3rd Ave. I went there recently with a friend after a run in Central Park and it was great. Burgers were crusty and juicy, fries were crisp (not hand-cut, but good nonetheless) and the Arnold Palmer was quite refreshing.
2.) Two Boots Pizzeria- 1617 2nd Ave. at 84th Street. Cajun inspired pizza place. Love the cornmeal flecked crust and the spicy tomato sauce. The "Bayou Beast" slice with shrimp, crawfish, andouille sausage and jalapenos is one of my favorites.
3.) Papaya King-179 East 86th Street at 3rd Ave. I'm not a huge fan as I prefer Gray's Papaya but it does have a huge following and it is one of those "when in NYC" experiences.
4.) Lexington Candy Shop-1226 Lexington Ave. at 83rd Street. Old school soda fountain. I usually sit at a stool the well-worn counter. Good malteds and egg creams. They have a full menu too. A bit pricey for the kind of food they serve but the people there are very nice and it is a experience that is sadly fading from NYC. Their website:
http://www.lexingtoncandyshop.net/ If you click on FOOD and then READ MORE it'll display their menu.
5.) Tal Bagels-333 East 86th Street bet. 1st & 2nd Ave. Good bagels and cream cheese. One of my favorite places to go when I'm in the neighborhood.
Hope this helps. Enjoy the museum!