L.H.
Hi J.,
I live in Fullerton too, and attended a birthday party once at the CSUF bowling alley. It was very private, you could bring in your own food, and there was something for everyone to do (billiards, pool, and plenty of space for folks to sit and talk).
The other place I thought of was at Concourse Bowling, next door to Fry's on La Palma Avenue. It is not at all what you think of when you think of a bowling alley. It's actually a very nice place for a get together and can be made to be very private for your party. We had a party there for my daughter's girl scout troop and everyone had a great time.
Wherever you plan your son's party, I hope it is a success and that you are able to enjoy the party too!
Best of luck,
L.