As someone who neither lives in San Francisco nor owns a car, I think SF would do well to construct a few new freeways to get a system that looks like this:
First off, it would ensure that all traffic that flows through San Francisco stays off city streets. This could be strongly encouraged by tolling everybody who exits the freeway into San Francisco. Furthermore, it would provide direct freeway access from all entrances to San Francisco to the Transbay Terminal, so busses from other counties wouldn't have to use city streets. Also, it would allow the narrowing and improving of Lombard St, Park Presidio Blvd, and 19th Ave.
Secondly, most new construction is either bored under existing neighborhoods or cut and cover, with the opportunity of new development/parks above through parks and low density neighborhoods. It also allows the removal of many redundant, above ground segments of freeway.
While I'm playing God, I would phase construction like this:
1. Remove the 280 from Mission Bay to the 101. Leave ramps intact for Southern Crossing.
2. Build cut and cover tunnel from 4th St./I-80 to 20th St./US 101. Then remove all the in between freeway and the central freeway stub and redevelop.
3. Build the tunnel project from the Golden Gate bridge, with ramps around Sloat Blvd for future eastward freeway.
4. Build the Tunnel from Mission St./I-280 to the aforementioned ramps. Then remove all of the 280 between Mission St. and Daly City and redevelop.
5. Build Southern Crossing (someday.) Be sure to include BART on it, probably starting at Fisherman's Wharf and following Van Ness to Caesar Chavez before bending southeast.