Yes, do take a look at the thread at the very top of this branch about Big Sur. Right now, the highway department says that the road will probably be fully open by Sept. 30. However, things can change, so keep an eye on the situation and be prepared for a Plan B if the bridge is not open.
You do not need a car in San Francisco. In fact, a car can be a liability. Parking is expensive and can be hard to find. There is good public transit and lots of taxis, Uber, and Lyft. The city is surprisingly walkable.
On the other hand, the LA area is tough without a car. I say "LA area," because it is really a sprawling metropolis of contiguous cities, of which Los Angeles is the largest. It can be done by transit, but it would be cumbersome and time consuming. Some lodging and some places you might want to visit will not be served by transit at all.
Mid-September to mid-October is when SF and the Central Coast have their best weather--warmest and most likely to be fog free. "Warmest" is a relative term, though, and you will need a sweater or looks got jacket.
Good that you got your SF lodging sorted. Besides the conventions, there are some big events, such as a free three day concert in Go,den Gate Park and a week of celebrating the Navy, including a free air show. If the local baseball team does well, there will be big playoff games going on.
If you have any interest in wine tasting, I can make some suggestions that are on your route, but not hopelessly crowded and expensive.
