Serious Pie on Westlake (maybe @ Terry?) is very good, but very busy. Fierabend for German is good (Yale Ave, at maybe Thomas? near REI). Agree w/Gingershelley on Tutta Bella above Whole Foods. I thought MIstral was good but overpriced, re:public is a good alternative at a slightly lower price but is definitely more a bar than a restaurant on weekend nights.
If you are attending something at the main building DT at the SW edge of SouthLakeUnion neighborhood, you could easily go down the hill just a bit to the Whole Foods Westlake complex and get some wine and pizza at Tutti Bella.
Second Bethwick's suggestion of Mistral Kitchen;; you could do aptz. and cocktails in the bar before a show.
A bit more of a walk, but also worth considering; oyster happy hour at Flying Fish, if you like them.
Let us know if your going to Capitol Hill space or SLU, can improve suggestions...
The nearest restaurants that I would recommend are Mistral Kitchen on Westlake Ave and re:public also on Westlake but north of Denny Ave. Check out their websites to see what appeals to you. re:public pushes the bar scene but also has really good food, younger crowd then Mistral Kitchen.