When are you travelling 'England'?
I'd echo a lot of what's been said.
Alcatraz definitely book early. At least two weeks or so. The Audio Tour is excellent.
Toss up where to stay in SF. Union Square and Fisherman's Wharf both have plus points. I stayed on the Wharf.
The Cable Cars are a must and if you get the chance go over the bridge to Sausalito. Fantastic place. Scoma's Restaurant is pricey there, but well worth it :-
http://www.scomassausalito.com/
On the way back, as 'Pubey' mentions, take the slip road up to Marin Point. If you go right to the top the views are something else. Same with Twin Peaks in the city :-
https://www.nps.gov/goga/marin-headlands.htm
Driving from Vegas to SF, I'd do it the other way. Start in Vegas and drive to San Diego and just drive the whole coast road to SF. You can add Yosemite as a side trip.
Plenty of overnight stop off points en-route or just lunchtime visits. Santa Monica for LA and then maybe Solvang, Pismo Beach and Monterey. Santa Cruz, even.
Definite must is the Nepenthe Restaurant on the Big Sur. Extraordinary views :-
https://www.nepenthe.com/
Have fun, mate. :thumbsup: