I have to agree that it would be best to get more experience (and perhaps additional training which incorporates gas management) before conducting dives in the 100-130 fsw range. Moreover, your buoyancy control and buddy skills should really be very good before conducting any deeper dives.
Rainer gives good advice with regard to being comfortable with mid-water (I call 'em "blue water") ascents where you'll probably need to rely on your instruments heavily. Understand that at La Jolla Shores, if you need to abort a deep dive, you'll almost certainly be doing a mid-water ascent.
At a minimum, please read and understand
NWGratefulDiver's essay on gas management at your earliest convenience.
After working on all of the above, you can certainly conduct dives at La Jolla Shores in that depth range.
The Secret Garden (100-110 fsw) is a fun dive site to check out. In my opinion, there's plenty to see there. The gorgonians are beautiful.
The neat thing about a Secret Garden dive is that you can hit other dive sites on the way back to shore. You can very easily visit an area I call the Crab patch (detritus patch at 60-80 fsw north of the Main Wall that's chock-full of nudibranchs, fish, and crab) and spend a few minutes at the Main Wall. If you are feeling adventurous, you can also navigate from the Secret Garden to the Main Point (Vallecitos Point). It's my favorite way to approach the Main Point.
There's also Scripps Canyon...which is an advanced dive site -- certainly not a site I would recommend to a beginner diver. That being said, Scripps Canyon is my favorite shore dive in the San Diego area. So much to see. It's always nice to say hello to the swell sharks there. Get at least 50 lifetime dives under various conditions before attempting a dive there. FYI, unless you have a key to the gate at La Jolla Farms, shore access isn't very convenient. It's a loooooong hike from SIO.
Have fun out there and dive safely...