I wouldn't hire a car for use in the city it's easy to get around without one, but if you do hire one drive across the bridge to Marin County and visit Sausalito which is a lovely waterside town with nice shops, cafes and restaurants (it's some years since I visited but hopefully it hasn't changed that much) you can visit some of the Vinyards in the area and the scenery is lovely further north.
I don't quite understand your comment about visiting Yosemite, do you mean as an outing from SF or later on in your holiday as I would guess that it would take up to 4 hours driving each way from San Fransisco leaving you not much time to see anything.
Hope you enjoy your trip it's a lovely part of the world.

you dont need a car for san fransico theres buses and trains to get you around,but the biggest reason is the cost of parking in san fran it is so expensive to park your car anywhere the rates are so high,

adding my two pennies worth - I wouldn't hire a car for the SFO part of your holiday either. You won't need it in the City and car parking is expensive.

Additionally, has anyone got any advice for doing a day trip? We're thinking about booking a day trip flight from Vegas in September.

When we went we drove into SF put the car in the hotel garage and then bought public transport passes. They did a 3 day one for $10 (it was 7 years ago mind). This covered the buses and the cable cars plus the mass transit system. The route maps are easy to follow and the buses frequent. There is absolutly no requirement to drive in SF.