Located just outside Downtown Palo Alto are a number of preserves open to the public. Foothills and Pearson-Arastradero preserves are managed by Palo Alto Open Space and the other surrounding preserves are managed by Mid Peninsula Regional Open Space. They all have different rules and regulations regarding hours of operation, trail usage, and vehicle fees, so it is a good idea to visit their respective websites before visiting one of the preserves.
https://www.cityofpaloalto.org/Departments/Community-Services/Open-Space-Parks/Neighborhood-Parks/Foothills-Nature-Preserve
https://www.openspace.org/
https://www.cityofpaloalto.org/Departments/Community-Services/Open-Space-Parks/Neighborhood-Parks/Foothills-Nature-Preserve
https://www.openspace.org/