This question came up from friends who were visiting last year, and here’s the list we gave them. I believe all of these restaurants are open on Thanksgiving, but be sure to call ahead for prices and reservations ASAP.
On the high end in La Jolla, there’s La Valencia, The Shores and The Marine Room.
I think the Rancho Valencia Resort in Rancho Santa Fe may also be open. I remember that we dined there with friends on several holidays, but can’t remember if any were on Thanksgiving.
Also try L’Auberge in Del Mar, and possibly Jake’s and Poseidon.
If you want a truly reasonable home-style Thanksgiving, Mimi’s Cafe is also open, I believe. They have several locations.
I’m sure other posters will offer their thoughts, but this is a start.