Having just got back after spending 4 days in SF I can say you should have a great time in the city. We were fortunate that we found a 'window' in the bad weather they've had on the west coast this month, floods and storms throughout January have been very unusual for them but the four days we spent there were cloudless which makes such a difference.
I actually think 10 days might just be about right to enjoy all the best places to visit. Buy a 7 day 'passport' and you can use all local buses, street cars and cable cars. I'd recommend you buy a 'Big Bus' tour on your first full day, it's a 24 hour hop-on, hop-off tour with 21 stops at all the major city attractions and is good for spending a short time at some places you wouldn't want to waste too much time visiting as a one-off, then just get the next bus to continue the route around town. It will also help you get your barings in town which is quite easy as it's a similar grid pattern to New York.
As others have mentioned there are all the well-known attractions worth visiting so I'll just add a few that I found worth seeing. We stayed in the Union Square area and at the top of our hotel, the Hilton O'Farrell St on the 46th floor of Tower 1 is the Cityscape Bar. It has a raised bar in the centre and steps lead down to the panoramic windows with seats all the way round giving virtually a 360 degree view of the city. It is open from 5.00pm - midnight and if you time your arrival about half an hour before sunset you see the skyscape change from day to night for one of the best views you'll see in town.
Close by are a couple of excellent restaurants. If you like steaks then John's Grill at 63 Ellis is worth a visit, over 100 years old it's a proper old style steakhouse on three floors and was packed out, the food was top-notch. If you like Indian food then the New Delhi restaurant at 160 Ellis is rated one of the best in the USA, I tried some of the house specialities and they were amazing.
We were fortunate to sail into SF under the Golden Gate and the views in the Bay area are breathtaking. So many different perspectives from the water so I'd strongly recommend a boat trip around the bay. Anyway, I'm sure you are already getting a feel for the place and have a good idea of what you want to fit in. Just be careful, it is an expensive place and it is easy to spend more than you bargain for. I'll just add a few few links to useful sites. The Bay City Guide is a booklet that is available in most hotel foyers and has many offers within, you can download an app which may prove useful. Have fun...
http://baycityguide.com/
http://sfhelicopters.com/
http://www.sftodo.com/boats.html
http://www.cityscapesf.com/