Every Friday evening for the rest of the Summer, there is now a wine stall in Friedberger Platz. The place can be pretty packed but the atmosphere is good, the crowd is relatively young and there is a good selection of wines for about €3 a glass. There is also a burger/sandwich stand there as well in case you get peckish.
Just beware, last drinks are served at 8pm and you have until 8:30pm to return your glasses.
After 8pm, you can move down the street to one of the classy little bars for further drinks if you are interested. Check out Weinbar Piccolo on Bornheimerlandstrasse for a good selection of well priced wines.