PS1 (
P.S.1 Contemporary Art Center) in Queens (G 21st Street) - Art and the 'Warm Up' (Best DJs and EDM ever) is a must
Brooklyn Botanic Garden (2/3 Eastern Parkway) - Cherry Blossom Festival
Prospect Park (2/3 Eastern Parkway) - Zoo and Circus
Union Square (4/5/6/N/R/Q) - From now until the end of summer you can usually find a farmers market, artists performing or vendors around (mmm, free cider! :09

.
Bohemian Beer Garden in Astoria (Off the N on Astoria) - Outside with Beer, meat -'nuff said.
Citifield for a Mets game
Other Places: Flatiron Building, Battery Park, Roosevelt Island Tram, Brooklyn Bridge, Central Park, Washington Square Park (if the renovations are complete - watch out for vicious (OK, "friendly") squirrels :09

... then walk around and hit one of the restaurants in the area that offer good deals on drinks and food (not just for NYU students).