I like Baltic, and it's very convenient for the Old Vic, though I have only been there post-theatre. It's modern Polish cooking in a very stylish setting. Service is a little inconsistent, and it isn't cheap, but it gets a thumbs-up.
Thai Silk is nice. Used to go there pre-theatre when it was on W'loo Road. Don't seem to think of it so much now it's moved (even though it's only moved a little way).
Waterloo Bar and Kitchen (20 yds round the corner from Old Vic, South on W'loo Rd) is good, and they are good at knowing when you're in a rush for pre-theatre meals. We went in a party of about 10, before going to the last but one thing at the OV, and they coped really well with people turning up late and being generally dizzy, clueless, customers (my friends, of course, but not me ;0).
The cafe in the Old Vic is quite nice as well (though it's been a while since I've been there).
I'd second Waterloo Bar and Kitchen - I've been before where they have really hurried things along to make sure we weren't late.
If you don't want something too formal I'd go for Inshoku Japanese on Lower Marsh - its good food and really cheap, especially for sushi. Its not glam inside but the tempura makes up for it. Ooh, I'm getting hungry now..!