We like the Seafood Grill across from the train station. Fresh fish, grilled, or in fish tacos. Avoid the fried stuff - oysters, etc. Also, in the same little center is Kentro, a new Greek place that is very good.
For Mexican, try El Camino Real, on Euclid, south of Chapman, in the Stater Bros center.
El Camino Real, 303 S Euclid Avenue, Fullerton
Seafood Grill, 100 S Harbor Blvd, Suite D, Fullerton
Kentro, 100 S Harbor Blvd, Suite A, Fullerton
Camino Real Restaurant
13756 Amar Rd, La Puente, CA 91746
100 S Harbor Blvd Ste D, Fullerton, CA 92832
I have not been in a while, but I always enjoyed Cafe Hidalgo when I lived there. There was a decent Vietnamese place over by the movie theater and Costco - Pho 89 or 99 or something like that.
Old Town has gone through a lot of renovations, so I would explore around there. If you like sushi rolls and teppan, Chomp is decent. It does not rate as one of my top sushi bars, but it is fun and they have a lot of inventive rolls.
Chomp Sushi & Teppan Grill
181 East Commonwealth Avenue, Fullerton, CA 92832
305 N Harbor Blvd Ste 111, Fullerton, CA 92832
Ma's Chinese Islamic. Technically in Anaheim, but surrounded by Fullerton on three sides.
601 East Orangethorpe Avenue
Anaheim, CA 92801