Depends upon the route you're taking..
Depending upon the route and time of year you're traveling you do have the option of seeing some amazing natural sights..
Just off the top of my head, not too far from your route from Roswell NM (why Roswell???)
-- White Sands National Monument (NM)
-- Carlsbad Caverns National Park, NM
-- Canyons de Chelley National Monument
-- Petrified Forest/ Painted Dessert National Park
-- Monument Valley (Arizona/ utah)
-- Mesa Verde
-- Meteor Crater Arizona
-- Sunset Volcanic Crater National Monument
-- Mojave National Preserve (including Kelso Dunes)
-- Death Valley National Park
-- Joshua Tree National Park
-- Mount Whitney/ The Sierrra Mountains (most spectacular from the East)
-- Devil's Postpile National Monument/ Mammoth Lakes (California)
-- Big Sur, California
-- Hearst Castle
-- Carrizo Plain, National Monument
-- Lake Tahoe (California/ Nevada -- a bit more out of the way, but very beautiful)
-- Hoover Dam (Arizona/ Nevada)
-- Sagauro National Park (near Tucson -- depends upon the route you take from NM to Grand Canyon)
-- Sequoia National Park/ Kings Canyon (near Yosemite)
-- California Wine Country (there are several regions)
-- California Spanish Missions (some of which are quite scenic)
-- LA area surfing, hiking, movie studios etc, sailing, snorkling, and the like
And along with this are more "exciting" options you can consider -- white water rafting, bungee jumping, offroad adventures (from backpacking to mule trips to 4 wheel drive expeditions), etc.
if you head more north, there are a different selection of sights to see and things to do -- Natural Arches, Escalante, Moab, etc.
And a couple of final notes
- There's also a Wigwam Hotel in Holbrook NM I've driven by
- Depending upon your interest, you can spend days in Yosemite -- but you'll need to do some walking. There's some absolutely wonderful hiking trails you can take, but some of them are at least a half day long or more.
Voice of Experience here.
On my first ever "real" road trip I made it from Shreveport to Carlsbad Caverns in one day. Watched the bats, did the tour the next morning and made it to Roswell. I think we spent all of two hours looking through Roswell before we decided that we needed a nap. We didn't wake up until well after supper time and missed a good bit of Roswell.
Anyway - stalk my posts I done a few similar trips starting from Shreveport so they should be of use to you.
Laura