There are thousands of miles of hiking trails in the Bay Area. I am not sure where they want to start. Here is just a sample of one web site call it the “best” trails.
https://trailtopeak.com/2018/12/10/the-10-best-hikes-in-the-bay-area/
Regardless, you should not rent a car, because one day of hiking is nothing in the Bay Area. For example, just from my back yard, there is a 100-mile trail that can take you to Fremont and or Walnut Creek, in East Bay Regional Park. On Pennisula, you might be able to hike from SF to San Jose. Uber or Lyft is your friend, use them. Plan carefully for a week or so, stay in the hotels along the way.