I think you my be underestimating the size of LA and it's urban sprawl and to be honest if you want to do LV to LA to SF in 2 days you won't be able to visit the coast and have fun, it would be Interstate for the most part.

Personally speaking, if I had such a limited amount of time I would avoid the hustle and bustle of LA and take one of 2 approaches. That would be to go from LV to the Morro bay area and enjoy the coastal route to SF [subject to status] or, from Las Vegas drive across Death valley on 190 to 395 and head North towards Mono lake and head West on CA120 over the Sierra Nevada into Yosemite on Tioga pass. This journey is as diverse, scenic and exciting as you can get over a 2 day period and will give you a break from City life and offer an insight to the incredible scenic beauty the US has to offer.