Have you checked with you SF DPW
Department of Public Works? http://www.sfdpw.org/index.aspx?page=644
According to the documentation, a permit is required, along with following an outlined process. The tree has to be approved as appropriate.
Friends of the Urban Forest have a Species Directory of the trees that are most likely to thrive on the streets of San Francisco. http://www.fuf.net/resources-reference/urban-tree-species-directory/
Their site also has many useful links, and has information to help you every step of the way.
Be careful. It may seem like a good idea, but just picking and planting a tree may get you in trouble if you circumvent the process. It may be a little bit of bother, but there are folks to help you along and make sure the tree won't be a problem down the road. Good luck!