There are three that come to mind that are right within walking distance of the Keswick. Athena Restaurant which is a BYO greek restaurant around the corner is ok greek food. GG Brewers is a brew pub/restaurant right across the street from the theatre, and on the corner is Keswick Tavern. There is a chinese restaurant called Queen right near the Keswick too but I have never had too much luck there.
For a quick sandwich there is a Primo Hoagies, (no room to sit down).
Beware all of them get VERY crowded before a show. I would personally not get there any later than 6pm for an 8pm show.
I am a fan of Union Jack's a pub about a five minute drive away from the Keswick. Good wings.