I think Nick failed to mention that as one of those fancy manufacturer Pilots he didnt fly some old piece of junk. It probably had AC, new smellin Leather and so much spending money in his pocket that Igor would have been embarrassed.....ha ha
Anyway there are a number of ways to do it, and the first is like your doing plan ahead. lots of folks here to give you pointers on what to see and where to stay. I just mentioned on another thread that I ferried a B206L3 down here to the caribbean from Tucson , Az a couple weeks ago. I would have like to have the luxury of time but it was business and no time to sight see.
Someone above mentioned the Grand Canyon and they are correct, if you go that way there is a lot of traffic and a lot of rules, besides being a place to get your butt kicked in Turbulence. Contact some of the tour operators in both Grand Canyon east and Las Vegas. Most Chief Pilots can give good advice or talk to tha FAA in those areas, they make the rules and can tell you what you face.
My email is good if your interested in some nice stops, but as I said your planning ahead will really be helpful for a fun and safe trip.