A few thoughts from a New Yorker that love the Bay area: with 4 of you and a car booked, if you plan your day's route ahead of arrival and map out various parking garages, you will cover more places behind your own wheels. For 1st. time visitor to SFO, finding parking can be a real headache - here's a useful link -
http://www.sfmta.com/cms/pgar/indxpkgar.htm
Among the rules to remember is to always check the various posted parking signs & rules, 100 feet to either direction on your side of the street, and turn your wheels properly when parked as there are lots of hills, and you will be ticketed for not doing so when you are on a grade. Another useful resource -
http://www.findingthesweetspot.com/pages/tips.html
Carry extra change (quarters) to feed the parking meter and if possible, get the $20 Parking Card. Watch out for residental zone permit parking, rush hour no-standing/stopping signs and street-cleaning rules, etc. - and if you see an empty & legal parking spot close to where you wanted to be, take it & exercise, walk the rest. Even for Chinatown, if you search the online website, you can find a garage that costs only $12 or $15 for several hours/all day parking if you are prepared to walk a little bit uphill/downhill (i.e. near the Broadway Tunnel. Metered and/or legal parking spots are hard to find but not impossible if it isn't lunch or dinner time with everyone else doing circles in the neighborhood - same for Pier & Fisherman's Wharf.
You can cover the Marina District, drive to the foot of the Golden Gate Bridge Vista Point's metered parking lot, and walk around & take photos, etc. without crossing the GGB, and turn around & head south on Presidio Pkwy to check out Golden Gate Park and/or China Beach, Land's End, Cliff House & down The Great Hwy along the Pacific Ocean with the beaches, stopping along for scenic spots before heading back toward Japantown & Civic Center, etc. Parking is fairly easy, either free or pull into a metered spot & feed it - and for a great view of the city, day or night when it's clear & not foggy, you can only get up to Twin Peaks in a car and/or ride in a tour bus - Muni doesn't get you to the highest spot within the city.
And, what better way to come down the crooked Lombard Street at Russian Hill - after checking your rental's brakes first.
Instead of spending a $100 on Bart & Muni passes, (for the same amount $$ spent) you could park at 4 or 5 different garages in different part of the city, walk the rest, and still have enough change to feed the parking meters and use the Parking Card - and see more for your short stay. BTW, we are heading out there in 3 weeks ...