I'm a little embarrassed to say I went to The High Line for the first time about a month ago--and it took a class field trip to get me there. Now it's one of my favorite places. It's got the winning combination of being a supremely done park, with proximity to great food that is easy to transport and picnic with (and no hassle of having to bring a blanket and a cooler). It also gives me the opportunity to explore the Chelsea Market, which I love, but never want to eat at, at least on a sunny day--it's too dark and cavernous. What we like to do now is walk around the market (a couple of our favorite spots are Dickson's Farmstand for sandwiches, 9th Street Espresso for iced coffee, and I just read that The Green Table is selling brown-bag lunches this summer) and then go sit up on the High Line. It's a pretty perfect combination. Afterwards, you can pop down to the Blue Marble Ice Cream Cart at the Standard Hotel , just on Washington and 13th Streets. They're from Brooklyn, and make some of the best ice cream in the world.
(I'm crazy about the landscape design)
(this stair area is a perfect spot to eat lunch)
(perfect family portrait opportunities--or your entire 1st grade class)
If you live in the NYC area, check out the High Line events page. They have free kid events on the last Wednesday of the month this summer, like a nature scavenger hunt and workshop with High Line gardener Andi Pettis.