I have visited Yosemite, both from the west and east entrances.
The roads are decent enough, even with twists and turns, they are still nice routes. Just take your time and relax.
From SF, a day trip to Yosemite is possible, but you won't be spending a lot of time in the park. Overnight trip allows a more relaxed pace, so you can appreciate the views and serenity of nature a bit more.
If you have time, take 120 to the east entrance (closed in winter so check if it's open). The route passes through high country and is very scenic. Outside the east entrance, you should visit Mono Lake and see it's tufa rock formation.