Perhaps need a car, but you if you get to twin peaks, good view of down town san francisco.
http://maps.google.co.uk/maps?hl=en...49,-122.446629&spn=0.006065,0.009645&t=h&z=17
The parks around golden gate bridge are worth a visit.
Presido and Lincon park
http://maps.google.co.uk/maps?hl=en...7.785504,-122.500477&spn=0.0485,0.077162&z=14
Should have no problem getting to them by public transport. Public transport in San Francisco is excellent. Only note of caution is that the buses are electric, braking and acceleration can be on the strong side.
Word of warning when I went in October 2001, I stayed at a hotel next to city hall. City hall is fine and the hotel was great. But just the next block down there was a porno cinema, and round the back of the hotel, cardboard / tent city for the homeless (probably has been shifted since I went there).
If you have a car explore outside the city, there's mt diablo, very little walking just a road all the way to the top and a short walk to the tower.
http://maps.google.co.uk/maps?hl=en...923076,-121.838379&spn=0.382405,0.607681&z=11
& Mt Tamalpais (I didn't go up this mountain because it was covered in cloud)
http://maps.google.co.uk/maps?hl=en....858862,-122.541504&spn=0.19137,0.303841&z=12
I know you said you wanted to relax, but yosemite national park is less than 1/2 day away by car (1/2 a day going Amtrak which is bus/train/bus), I've been to several national parks but yosemite is very impressive.
Final warning, weather can be very random. When I visited in 2006, the day I left the weather was like this
http://www.flickr.com/photos/61808487@N00/1423705491/sizes/m/in/set-72157602114015980/
Probably about 14 C and overcast, drove from just North of Golden Gate bridge to the airport. At the airport, blue sky, sunny and +21 C. So you need to be prepared for a wide range of temperatures.