Well, there are really only two routs:
You take Hwy 580 east to Manteca and you can either stay on Hwy
120/Hwy 108 for the northern route which is about 190 miles and
typically takes about 4 and a half hours
Or the southern route where you head south on Interstate 5 and cut
over to Merced and then Hwy 140 into Yosemite. Its about 210
miles but usually takes about the same amount of time because the
40 miles on Hwy 140 is a little easier drive.
I think the northern route is prettier but once you get out of
Merced, the southern rout is beautiful, too.
If you leave SF very early and beat morning traffic youll be very
close to the four to five hours travel time and could get to
Yosemite by noon.
Sept. is typically slower than the summer peak season - seems
reasonable to get a place without reservations.