There are a couple of Sport Chalets near where you're staying, and they have a fairly large rental department, especially the one on Midway, because they have an on-site pool. Here's a link to the three closest.
http://www.sportchalet.com/corp/index.jsp?page=storeLocator&zip=92106
The Shores, as mentioned is a good location. If you're not used to looking for (and finding) the wealth of life that lives in the sand and detritus, you won't see much unless you start down into the canyon. Straight out and South from the main Lifeguard tower, you will encounter some great rock structures starting around the 50' contour, and continuing South towards Vallecitos Point.
The Marine Room reefs are an excellent shore dive, but they're shallow, so you'll need calm seas and a 2'-3' high tide or larger to dive there. Lot's off rock /reef and kelp structure with tons of life from large to small.
La Jolla Cove is another excellent shore dive, but there are stairs down to the beach, and the Cove itself is seldom clear. Using the Cove as an entry point works well though, and you can head straight out towards the yellow buoy, or turn right passed the Cove and head East along the cliffs and caves. Entry and exit are steep, as the Cove gets deep (relatively speaking) close to shore. It's an easy entry / exit though if the Cove is calm.
Good luck and have fun!
