There are actually a ton of restaurants in the Civic Center area since this is where the theater district is largely located.
Here are what I would call the three best Civic Center restaurants--I don't know if locals would agree:
1. Farallon: A seafood place.
2. Brenda's Soul Food
3. Pegolac: A vietnamese place.
These are all delicious and there are a ton of other ones as well--a lot of them fairly divey since you are bordering the Tenderloin.