A cheap motel room plus one day car rental equals a good hotel room in the city itself so you will probably not save any money by finding a low priced motel outside the city.
Normally at least one of the buses from the train in Emeryville will stop right in front of the Hyatt near Market Street.
We live in the city, have no car, and use Muni for everywhere in the city itself, Caltrain, BART, Golden Gate Transit, SamTrans, VTA, etc to get around the rest of the area. Get a good detailed map of the region, figure out where you want to go and then go to the web sites of these various transit agencies. I almost forgot, there are also ferries to various places around the bay. As a part of that: Ferries out of the Ferry Building are cheaper than those out of Pier 39. You get some excellent views of the bridges, Alcatraz, etc, depending upon which ferry run you take.
There are frequent trains between Emeryville and Sacramento. State supported. Look for Amtrak California.
All the transit agencies here have web sites that give you maps and schedules. Some are easier to navigate around than others.
For many of the Muni routes the service is frequent enough that there is no need to bother with the schedule. Just get the route map.
Market Street has about every form of public transit known to mankind.
Diesel bus (Muni)
Electric bus (Muni)
Streetcar (Muni) - mostly restored PCC cars, some from foreign places
Light Rail (Muni) one level down below street
BART two levels down below street
An aside: The BART tracks are not standard gauge, but wide gauge, 5'-6" to be exact, which is the same as Indian Railway Broad Gauge, although I would suspect that the people that chose the track gauge probably did not know that.
Parking in San Francisco: hard to find or expensive or both. the meter checkers are agressive and the fines are high. traffic is slow. route signage in the city is hard to find or non-existant.