I was out in vegas recently and was simply AMAZED by the number of cyclists on the road to the Red Rock canyon scenic road. The shoulders/bike lanes seem very nice and wide and the roads are smoooooth. It would be a lovely dream to ride those roads, I think. Lots of people out cycling and doing long runs. Just be aware that you will want to start early because it will be HOT. We had a abit of a hot spell when I was out there and it got to over 95degrees (in late april!) and the heat is simply brutal. You can refill bottles, though, at the visitors center.

have fun!