So, in Fullerton, there’s a couple that don’t work because of your restrictions. Summit House and The Cellar are primarily Steak, although they both have fish, and probably a chicken option too. But not a lot of selection once Steak and Fish are omitted.
Mulberry Street is good for upscale…
The Packing House is a great place for a food adventure. If you're looking for a good brunch spot, I highly recommend Poppy and Seed. If you have transporation, totally agree that Bottle Logic is worth a stop and the Orange Circle. It is not in Anaheim but it's a great place to walk around with shops and restaurants.