I'm from San Diego and, yes, the beaches are free and gorgeous. There is a commuter train that goes up the coast, aptly named The Coaster, that can take you up and down the San Diego County coast. You can explore different beach communities this way.
Another "free" option is Balboa Park. It is an amazing collection of gorgeous Spanish architechture, stunning gardens, and is also the home of San Diego's best museums. You can just walk around the park and relax for free or you could even visit some museums (try and find out their free days). It is right next to downtown.
Balboa Park is right next to the world famous San Diego Zoo. While the zoo isn't free or even that cheap, it is amazing and a great way to spend a day.
If you will have a rental car, there is a great beach/cliff/nature are called Torrey Pines State Beach/Reserve not too far from the city area. Great hiking and scenery.
My personal favorite thing in San Diego is to actually head out to the Anza Borrego desert for hiking and even star watching. It is a 2-3 hour drive, though, and will be very hot this time of year.