Ok Mr Red, you got it given stars are playing silly buggers at the moment.
My trip involved having the car for a calendar month, I didn't have it in Vegas. The bit I would cut out of my trip is going far south as San Diego which I did via Phoenix. The problem with this is you end up double backing on yourself a couple of times.
The Grand Canyon south rim is a days drive from Vegas, I stayed in a place called Williams which was a one horse town about 50 miles from GC itself. You will drive right past (used to be over) the Hoover dam this way, which deffo worth an hour or two admiring. I reckon you will want a whole day at the canyon, watching the sunset is of the things to do there as the rocks change colour in the different lights. You can do Sedona the next day and head back west after.
Problem is the natural way to go back to SF is back thru Vegas now. After this it is probably a long days drive to the foothills of the Sierra Nevada. In theory you can do this through Death Valley but in the height of Summer the weather is going to be ludicrously warm. I would head up the Owens Valley on the East side of the Sierras, which is pretty unique place as it suffers from a massive Rain shadow from the mountains. There are few things to do before entering Yosemite this way, I went to Bodie which is a ghost town from the gold rush days which was very erie.
Tahoe looking at the maps maybe a bit out of the way and not within your time constraints, it is probably a days drive each way North from Yosemite. It is probably straight choice between this and heading across the Californian central valley to the Pacific coast just north of LA. I would go with the latter but they are both great choices. With the latter you could also do the very underrated Kings Canyon and Sequioa national park which has the worlds largest trees as well as more amazing vistas etc.
If you do the coastal route depends where you join, I personally am not a fan of LA. It lived up to its reputation as the Worlds biggest car park and is a very fractured City imo. Santa Barbara however is really nice which is 100 or so miles further up the coast, it has a lot early 20th Century Spanish architecture. From there you just head north following route 1, for a few hundred miles till reaching SF. Numerous things to do en route, but the best thing is just pulling out into layby's and admiring the views. You have to stop at the Waterfall that falls into a private beach and straight into the pacific.
You will not need the car in SF, in fact it will be a hinderence more than a help. I highly rate the official Alcatraz tour, there is only one company who actually dock at the island. Book in advance through
http://www.alcatrazcruises.com/ online before going as they often sold out. Best way to get around is the various public transport, get a MUNI ticket for 3 days think it was $20, that gets you on everything (exc BART) including the Cable cars which you obviously have to do.
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