This Traveler Article has a link to a map with a list of hotels that offer  Free Parking or Parking Packages and are mentioned often on the Trip Advisor San Francisco Forum. 

Most regulars and Destination Experts strongly suggest that visitors not have cars in the city or just park their cars and use public transit to get around SF. 

The list of hotels on the map is separated into two lists,  one which has parking included in all their rates (could be construed as free parking) and others which offer room packages or specials which include parking.  These packages may or may not cost more than their discounted room only rates

There are plenty of other hotels which may offer parking packages so it may be best to search hotel websites for deals.

It is always a good idea to  check Trip Advisor Hotel Reviews before you book.

The Map  with the hotels can be found here