Hmmm... summer in the City on weekends can be a treat - oftentimes, the folks who just don't want to deal bail out in favor of the beach or the mountains, so it might not be as busy as you think.
My DD loves the Ancient Playground next to the Met (part of Central Park) but that's in an entirely different part of town from the High Line park.
I've wandered into Chelsea Market and it's fantastic.
Chelsea Piers is a lot of fun; I had a team outing there once! (We all had lunch together and then went bowling.)
There are a lot of great green spaces throughout the City. Say what you like about Bloomberg (and I usually do), but his Greenways plan went a long way towards improving access to parks and physical activities around the perimeter of Manhattan! You walk (or bike or skate!) almost the whole way 'round the island without setting foot on a City street. (It doesn't cross uptown, which is a bummer, but if you exit near Riverside Church, you're not far from Grant's Tomb.)
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Liz
DD (3/2010)
"Make mistakes! Get messy!" - Miss Frizzle