The Fifth and Mission Parking Garage (which runs the full city block from Fourth Street to Fifth Street) has its own website:

http://www.fifthandmission.com/


Since you're staying at the Palace, you'd want to park as close to the Fourth Street end of the garage as possible Iif you look at the picture on the website home page, the corner with the curved glass facade is the Fourth Street end of the garage). It's $22 for up to 24 hours.