It's not the closest to the attractions you want to visit, but if price is no object I'd suggest the Hotel Del Coronado on Coronado Island. Great hotel with a great beach and pool.
Ditto on the Del if you can afford it. It will give you the most full resort experience although (unless they've changed in the many years since I have visited) the dining rooms can be stodgy.
I dont think the Del has rooms that sleep 5... I am so tired of seeing Exceeds max children!!!!
We have opted for the Embassy Suites, since they have a nice breakfast. We are staying in the on e in La Jolla as appose to Downtown. We have a car, and the LaJolla one is cheaper lol