When a place is very nice and very popular one of the biggest problems is finding a parking space. In La Jolla, especially in The Village and at the beach, this is frustratingly true.
However, there are 13 parking lots/structures open to the public and Valet Parking which are also open to the public.
Otherwise, street parking is free and the competition is so high that one must be detremined to remain calm and collected while driving around the block many times or the desire to leave will rob one's chance to see what all the excitement of La Jolla is all about.
La Jolla is not the place to go if you want to get around by public transpotation. Of course, if your plan is to stay only on the beach, or only in the downtown area, than a car will not be necessary. However, there are too many things to see and do. Limiting yourself would be a shame.
Rent a car--or drive your own--but make sure you are able to explore all of La Jolla, not just one small section.
If you want to make an impression when you drive up to the valet at La Valencia, rent a luxury car just for the fun of it.
You'll almost certainly drive to La Jolla. Once you're there keep in mind there is free parking on the street, but if you can't find a spot, look for the blue parking signs that will lead you to a lot where you'll pay an hourly rate that will be posted.