I rented a car from the airport in San Jose del Cabo and used this to get to San Jose and around San Jose. I really didn't see many other options for getting around. Without a car you are really at a lose because travel between San Jose and Cabo San Lucas is about a 15 minute drive. There didn't seem to be much of a bus system either or local transport. Luckily, you can rent a car pretty cheap if you look online or aren't worried about style.
If you're looking to save some money and have extra time to spare, you can walk to the bus stop about 3/4 mile from the airport and take the local bus into San Jose or Cabo San Lucas. Go right out of the airport and cross the road (small cantina, stop for liquid refreshment), then down the hwy on the left side of the bridge you will see the covered bus stop. It was about 20 minutes and 10 pesos to San Jose a little more than that to Cabo. We were heading to Todos Santos so we took the Aquila bus from San Jose (see Todos Santo page).