I read that San Diego doesn't have any international flights leaving at night - which is where day rooms come in handy. People who fly in on a domestic flight and then take off maybe 8 hours later to far flung places. The hardest part is what to do with your luggage! Pre 9/11 there would be luggage lockers. No more! I had about 8 hours in the Boston airport recently, between flights. Thought I'd be able to entertain myself but around the 5th hour I'd kinda had it.
AND most of the restaurants are on the other side of security - airside. I used info from this website called Sleeping in the Airport. At least it will help you find out comfortable places to stretch out:
https://www.sleepinginairports.net/usa/sandiego.htm
I'd be tempted to go to the the tourist info or that place with the phones for shuttle pick ups and call a couple hotels when you get there and just ask. From what I read you can walk to downtown from the airport. Pack light???