Lady Blue lived down in SD for years, and I just saw her in another thread. She can probably give some good thoughts on the best way to see Tijuana
As for lodging, go to Orbitz and do a hotel lookup. You'll see a variety of decent hotels, along with a variety of prices. I personally try to avoid traveling where I spend as little as possible... that usually feels to me like an effort to be miserable in someplace nice. I just took a look on Orbitz, and found prices ranging from $50/night to well over $400. In general, I'd feel comfortable at any place between $75 and $125...
Remember that LA is huge, and has correspondingly huge traffic. It's worth it to spend a couple bucks more to stay near where you'll be that day (or the next).