I will be in San Francisco from Oct 10-14 and I would love to visit the park for the day ( most likely Sunday the 12th) Is this still a good time of year to visit? I am planning on renting a car at SFO (only place that is open 24 hours). What would be the best route to take and what should I see in my limited time in the park? Is it worth the cost of renting a car and paying the underage drivers fee of $20. The total still comes out cheaper than a bus tour, and I would like the freedom of going at my own pace. Thanks!

Ordinarily I would discourage somebody from visiting Yosemite in one day driving from San Francisco and back. Why? It's crazy. It's way too much. However, since you are under age, you are at the time in life to do things that are crazy and way too much. Go for it.

The fastest route is the obvious one: 80, 580, 205, and 120.

HTtY

PS Have you driven down Higway 1 through Half Moon Bay, Carmel, and Big Sur? If not, that would be my choice for what to do in a too-long day. The drive to and from Yosemite isn't very thrilling.

Since it is about 5 hrs drive each way you should not rule out taking a bus tour.

If you can find one that will allow you to explore the park on your own and meet up with the bus for departure back to SF that would give you the freedom you want and also save you the effort driving.

This is the way to do it by using Amtrak bus, San Joaquin train and YARTS bus to Yosemite.
Board the Amtrak #6612 bus at 7:05AM outside the Ferry Building in SF. The bus takes you to Emeryville to board the #712 San Joaquin at 7:40AM. You arrive in Merced at 10:35 and the #8412 YARTS bus leaves for Yosemite at 11AM. You arrive at Yosemite at 1:25PM.
Your return trip bus (#8403) leaves at 6PM (don't miss it).
You get back to Merced to catch the #703 San Joaquin leaving at 9:15PM. The #703 gets you to Stockton at 10:25 to board the #3403 bus to San Francisco. You get back to the Ferry Building at about 12:35AM Monday morning.
The round trip fare for this adventure is only $72.
The question is is the trip worth it for at most 4.5 hours in Yosemite?

I wonder why so many travelers are eager to drive 10 hours round trip from from Los Angeles or 8 hours roundtrip from San Francisco to see Yosemite, and they are so mush less interested in making the 5 hour round trip drive from Las Vegas to Zion National Park--which, in my view, is as memorable experience as Yosemite.

HTtY