I would contact the rental company to ask if you can take the car into Mexico. However, Mexico is...well...it's basically a third world country and you really have to be careful where you go, let's put it that way. If it was me, I would probably look into a coach trip instead as there is safety in numbers! In all seriousness, Mexico is fine but there are areas to avoid, not to mention the language barrier if you don't speak Spanish, hence my recommendation of the coach trip.

I live in LA and would be happy to answer any questions you might have. I noticed LA is not on your list... for shame! Actually, LA is not for everyone so that's okay. Mind you, it's only a couple of hours from San Diego, so you would easily have time to spend a day or two in the LA area when you are based in San Diego.

Anyway, you asked about hiring a car... you don't HAVE to do it but it would be advisable. Otherwise, you would have to fly between all your locations and that would be considerably more expensive than hiring a car. Also, having a car is obviously much more convenient too. Make sure you are allowed to take the car out of state, since it looks like you would pick it up in Nevada (Las Vegas) and return it in California (San Francisco).

I would definitely go on an organised excursion rather than DIY to Mexico from San Diego- you should have plenty of choices to places like Tijuana for touristy shopping or Ensenada- shopping,beaches. Do some reading about those resorts before you go. I love Mexico and Mexicans but it is very different to the brochure photos.