Here's one: adventure.everydaycalifornia There's probably others as well- I just Googled "La Jolla Kayaks"

You have plenty of launch locations- go for it!

There are several companies operating Kayak tours. You can check under "Activities" on Trip Advisor or Google Kayak Tours La Jolla. Several operate year round, though sometimes only on weekends in the winter. It can be cold, though and this winter is much more rainy than usual -- so check the weather and dress accordingly! (By the way, the tour companies say they take tours of the caves. The kayak's don't go into the caves. They go past a number of shallow caves and usually stop outside and peer into the big cave. If you are kayaking on your own -- you can go through the cave (only about 30 feet wide) on one side and come out the other BUT, on weekends there will usually be a lifeguard or kayak company employee telling you you can't (because the don't want the tours going through so they just exclude everyone) and, if you're doing it on your own -- do not enter if water levels are low or if there is any sort of surge. It can be very dangerous! You should only attempt it in flat water where the cave rocks are well covered by water and when there is no surge. And even then it is not for amateurs! Have fun.

I don't know how far you want to go or the disability factor. I think you can be on top at street level and look down on the beach\caves. However if you want to go on the beach and closer to the caves there are stairs and uneven terrain which may make it tougher for your travelling partner. Perhaps best to call the La Jolla tourist center. Best of luck.