When the sun is out, Volkspark Friedrichshain is well frequented by people but never overrun due to its enormous size. If you are looking for for a quiet spot to have a picnic, you will certainly get lucky on one of the big recreational greens, by the romantic swan pond or the famous Fairy Tale Fountain.
Should you wish to do a BBQ to go along with your picnic, there is an official BBQ area on Kleiner Bunkerberg. And in case you run out of beverages or pretzles halfway through your picnic, supplies can be purchased at the Biergarten Schoenbrunn in the park.
If after all that food you feel like being active why not make use of the sports grounds of the park, for example with basketball, football, or beach volleyball. There is even a halfpipe and climbing wall for more extravagant desires.