Hello and welcome to R.T.A

We are renting an RV in LA and plan to drop it off in New York we are planning for 3 weeks which i think may be enough time??
Where as you have enough time to do this cross country trip you could spend this much time in California, Nevada and Utah for example and only just brush the surface of things to see and do, the States offers so much and distance's are vast compared to what we are used to here in the U.K.
From Vegas you have so many parks around it will make your head spin, there is Death valley, Zion, Bryce canyon, Grand canyon and Monument valley to name but a few, all providing different and awesome scenery, little towns and Indian lands. You could then hit Colorado and once again there is a million and one things to see and do , and it goes on!

I think your best bet would be to do more research and start looking for "must do's" and then try and piece them together into order and come back with a rough itinerary and we can then help you piece it all together.

Regarding the R.V, it's a great way to travel [the only way for me in the U.S.A] but make sure you do your homework on the costing, there are a lot of extras on the initial hire price and adding to that a return of 10 m.p.g on fuel, it's quite an expensive way to travel with just two people, and check out the extra charges for the "one way fee".