May C.
Yelp
There are two places near Burkliplatz that one can have a nice BBQ/picnic on a warm day: (1) Arborteum near Enge, or at (2) China Wiese [in front of the Chinagarten] near Bellevue.
The arboretum is the right place for those who want to show off their booty and immerse in a "fun to be young" bikini frisbee/volleyball/football crowd. It is a place to see, and to be seen. You can also BBQ/picnic there, but the land area is smaller, and is shadier/cooler.
If you are looking for a much bigger stretch of land with more sunshine then you should head to China Wiese. China Wiese is also more geared to a mixed crowd, from families, couples, friends, groups, etc. On the weekends you can also catch the excitement of watching tight rope walkers practice their gig, which is missing from the Arboteum since there are less trees.