Almost everywhere is possible to get to in San Francisco by public transit, however, some outlying areas take longer or are harder by public transit than with a car. How long various areas take to get to also depends on where you are staying. I'll assume Union Square since it's a common hotel location.
Twin Peaks is probably on the top of the list since no public transit vehicles go all the way to the to parking lot nearest the peaks. You will need to walk up a ways up if you go to the nearest transit stop and it's not on a major bus line.
The golden gate bridge is another spot that may be easier with a car because it takes two buses from the union square area on most days.
Lands end, the cliff house, Sutro baths, beach chalet are all in one area that is a long bus or streetcar ride (45 or more minutes) from downtown. The far west end of the park is also in the area.
The presidio may be an interesting place to drive through before or after the golden gate bridge, maybe on the way to lands end.
The palace of the legion of honor museum may be an out of the way place without a car, though I believe sometimes their lot fills up on busy days.
In general, places on the far west side of the city near the ocean may be more convenient with a car than without. If you were planning to go to Sausalito, Muir woods or the Marin headlands (across the golden gate just outside San Francisco) a car is nice. Most places east of the golden gate park are generally pretty reasonable to get to on public transit.
We don't know which places were on your schedule to see, but these are some common places that may be easier with a car.