We bought a TV antenna about 8 months ago. With a one-time purchase, we get free broadcast TV for the rest of our lives. Now that I see how easy it is to get TV reception for free, I feel like a fool for having paid for it all these years. It's a learning curve at first to get it all figured out, but so worth it once you do.
I don't live in the Bay area, so I can't advise you about the terrain around there.
Here are my suggestions:
Go to the website TVfool.com
Put in your zip code and it will tell you what channels you can expect to receive if you buy an antenna. It will also tell you what direction you need to point the antenna.
Buy a mohu leaf antenna. They look like a placemat and you can hang them on a wall or in a window. They are about $30. Buy 20 or 30 feet of RG-6 cable, which will be about $20. (Or, for now, to experiment, just use the comcast cable). Hook one end of the cable up to your TV, and the other end to the antenna. It is very very important to point the antenna in the right direction. Ideally the antenna should be up high in a window, or up high on an exterior wall. Play around with placement of the antenna until you get the best location for you figured out.
There is a website dedicated to people in the San Francisco area who use TV antennas to watch TV:
https://www.avsforum.com/forum/45-local-hdtv-info-reception/369015-san-francisco-ca-ota.html
I get my TV guide listings via a website called titantv.com
Surely you will get enough channels with an antenna to make it worth the $50 you spend.