Your profile lists that you are in Maryland. Assuming you are leaving from there, allowing only 4 days to get to the Grand Canyon is tight. You will drive all day and more.
I use Travelmath to do a quick calculation of distances and stopping points. Nice site, here is the link,
Travelmath trip calculator
Baltimore to the Grand Canyon is about 2300 miles and Travelmath estimates about 35 hours of driving.
Essentially getting across the country to Denver will probably involve the interstates. Once in Colorado you have several options:
(As you have more time going back, some of these places can be seen on the return trip)
1. Across Colorado, down the edge of Utah to Arizona
From Denver, continue across I70, actually a nice drive, to Utah where you have Moab are which has Arches NP, Canyonlands NP and Dead Horse State Park. Arches has a nice drive and easy views, Canyonlands and Dead Horse involve more getting out and walking to see the vistas. From Moab, head south and then south west to the Grand Canyon. The route is fairly obvious.
2. Go diagonally across Colorado to northern New Mexico then over to Arizona
Route 285 across Colorado is very nice. You will go through some nice places in New Mexico; Pagosa Springs and Santa Fe, which is a great city, lots to do, and the food is so good there. Then to Flagstaff and up to the Grand Canyon.
I f you have never driven in the southwest, be aware that as you look at a map, there may be roads that seem more direct and go from point A to point B, but they may not be suitable for an RV. Gravel roads in particular can be challenging, as well as high mountain passes. Not to say that it cannot be done, but rattling and shaking in an RV for 50 miles is not enjoyable, nor are blind curves and hairpin turns. One thing I have done to research a road is to look on wikipedia and there is usually a good description and often pictures to help you plan your route.
Arizona, Utah, Colorado and New Mexico all have nice state parks. One can often go in, take a quick look, take a short walk, have lunch and travel on, and some even have campgrounds. I use state road maps and state tourism sites to check out the state parks.
Moki Dugway (old uranium mine road, now a public road)
If you do plan on coming from Monument Valley be aware that as you travel north across the desert you will eventually come to a mesa in front of you with no obvious pass or tunnel. It is a 3 mile gravel stretch called the Moki Dugway, as shown in the post above. BE WARNED-this is challenging driving and it essentialy goes up the side of the mesa in a series of hairpin turns and blind corners with no guardrails. The hairpin turns do have a wide shoulders, but they are still challenging. I have driven this 3 times in cars and just this last September I was in a 2 seat convertible sports car and I felt confident. but I would to want to do it in a truck, van or Class B RV. Doable, but no fun. Also if you go up the Dugway, you will be on the outside edge and your passenger will be looking at the desert floor hundreds of feet below. If you love a challenge, as I did, its a great drive...in a sports, car not an RV!
See the picture below of what to expect.
One last suggestion, once you get to the Grand Canyon take 10 or 15 minutes and walk down the trail. Going into the canyon is so much different that being on the edge and looking down. Its worth it, but remember, "what goes up must come down" and in this case the opposite is true so plan on doubling the time to come up, especially if it is hot.
There is nothing like the scenery and rock formations in the southwest, especially northern Arizona and southern Utah to make you say "Wow".
Enjoy the trip.
Maryland to Grand Canyon in June 2017
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