Of course,what our US friends forget is that for an outsider driving a car across the States can be a really enjoyable way of seeing the country.
I've driven NY-West coast three or four times using auto-driveaway ( Febs2 - that's a way of driving other people's cars cross-country for the price of just the gas ).
You're normally given a week to get from coast to coast and it's quite possible for two people to cover 800-1000 miles a day sharing the driving doing all the boring bits in the middle leaving you time to do both Las Vegas and the Canyon.
The cars are normally in good condition and for a stranger to the States just driving along listening to the radio and looking at the scenery can be very relaxing.
www.autodriveawaydc.com will give you an idea ( you can either start in New York or train it to Washington/Pennsylvania ) and
www.roadsideamerica.com has some interesting diversions along the way.
Good luck.