The problem about the parks in Beijing is that they are always quite busy

However, 2 of my favourites are: 

Longtan Park - east of the Temple of Heavan

Purple Bamboo Park - Haidian district

both have plenty of trees, which are ideal in the summer, and you can usually find a place to sit

However, beware the groups of singing people

Don't parks charge admission and too much for a park, they should be free.

Purple/ Black Bamboo Park (the Chinese says purple, the English says Black for some reason) is free, and there are tons of other smaller parks that are free and not too crowded, like tuanjiehu park near Hujialou, and Rendinghu park north of Gulou dajie station :D 

Chaoyang Park is still the best park for picnics/ lounging on the grass as well as the olympic forest park