Well your looking at big area that is underpopulated. look here for some parks National Park Service - Experience Your America
. I will try to do this by state most places I have been some im looking to go. One thing to rember some places your looking to go can top out at 130F (54c). Get a park pass for a year it will save you time and money. https://pwrcms.nps.gov/pwr/fees_passes.htm
You will be starting out in Nevada so lets start there.
Las Vegas: sin city it self lots of fun if you like what they offer. Lets start slow
Hoover dam: huge thing 7 billion tons of concrete if you cant stand the heat here it a short run back to LV
Death Valley: it gets hot there -282 feet lowest point in the USA its in California but your so close may want to go there in the vary early morning.
Nevada test sight in near LV my want to take a peek 900 or so nuclear bombs tested there. dont know about getting out and about there, while we are on military things there are bases, testing grounds and target ranges all over Nevada if a sign said stay out. Stay out. lots of UFO sighting and new plane testing happens in the state. Area 51 - Wikipedia, the free encyclopedia
Reno area is better biking than a lot of the rest of state in summer. There is the old west town of Virginia city, Lake Tahoe cold and clear, Pyramid lake and its odd fish and the hole of a town and its state capitol Carson city.
A nice state to go in winter but can be hell in the middle of summer your on the western side of the Grate Basin the big empty it has some grate places separated by miles and miles of nothing bring water and stay away from caffen. Riding here different more like and endurance test. Can be rewarding or a great disappointment.
Utah to get here you made it threw the nothing and in to a state that has much to offer. The people here may be more conservative than others.
First the parks
and the Moab area
All grate and different.
There is also
The grate salt lake and its city the Temple there is something to see
Natural Bridges National Monument
Utah 12 scenic byway a ride worth the time
There is a lot to see here most of it starts to look the same. heres a link of someone with the time to see it right The Oasis Of My Soul » » My Archives
Colorado the mountain roads here are some best anywhere. It can get much colder here than farther west where you stared.
One of the only Interstates worth going on is I70 in the Glenwood Springs area.
There is the San Juan Skyway loop a grate ride. This road is one any one going to the HU meeting must take pass some place of note the town of Telluride, the Derango to Silverton train if your in to train its worth it im told and Masa Verde. it also sets you up for easy side trips to 4 corners (silly and stupid but 4 states converge there) Black Canyon (because the sun can shine there much) and Dinosaur Valley. Just riding the mountins roads are grate fun.
Wyoming much of this state is flat nothing bad news you may have to cross some it. Gut in its northern area are some of grate parks.
the grate one
Yellowstone and its lesser known one
Can be a slow go with all the people going there look out for the traffic there stopping to get a shot of some poor animal thats looking for a hand out.
one ride you can take is one that pass threw Grand Teton called Centennial scenic byway
other places to go Buffalo Bill center in Cody
Medicine Wheel Natural Historic Landmark
while your there you can go in to Montana and see where Custer got his at the Little Bighorn Battlefield National Monument not much to see if your not in to that sorta thing.
city that has there look with laws forbidding new construction to clash with the old, funny in land of the free but there you have it.
Roswell they have that UFO thing.
Los Alamos USA built the worlds first atomic bombs here.
lots and lots of old Spanish missions.
but its the desert and mountins people come to see such as the Gila Scenic byway.
you can pick up route 66 and take it back west to finish your trip.
America's Byways®: National Scenic Byways Online
Top US National Monuments: Travel Guides and Reviews | GORP.com
Maps of Parks in the Southwest and Western USA - DesertUSA
One thing in the west espechialy rural areas you will see people with guns most are law abiding its may be a little odd for you at first but thats the norm. Just you may not want to start a political argument with them.