I use a trip planner for this, started with Microsoft Streets and Trips, but that is no longer available. I am now using Delorme Street Atlas from inside their Topo, but there are also online tools. You want one that lets you put in a sequential list of destinations. Before computer tools, I did the planning with maps, as early as 1960 for family road trips. Computer tools made it easier because I could put in all stops with time for the stops, set a 50 mph speed for progress in moving, and thus could figure out where I would be at the end of each day.
You have to figure out what "out west" means to you, and what you really want to see. If it means all the way to the Pacific Coast, 3-4 weeks is probably just enough time for a loop using one route going out, another coming back, but not much time staying anywhere. You might have time to stop and see something every day, 200-300 miles of moving, 2-3 hours stopping, and a bonus if you manage to overnight in someplace interesting to you. Indeed, overnighting in an interesting place can almost double your sightseeing time with little impact on time available to travel.
Two 2-3 hour stops every day, you will move about 100-200 miles a day, which might get you to the Rocky Mountains and back, but you can mix in a few days like that and still get to the west coast.
You see the most on a loop. For example, on a Detroit to Los Angeles trip, my wife's family (Summer before we married) went Route 66 going out, with detour through Las Vegas, and came back further north through the southern Utah national parks and across US-50 through the Rockies, southern Colorado. My family's 1961 trip Detroit to western Montana went across Michigan U.P and northern Minnesota, N. Dakota and Montana going out, Wyoming, S. Dakota, southern Minnesota coming back.
My 2007 trip from NE Oklahoma was west across southern Kansas and southern Colorado (US-50) to the national parks on the Colorado Plateau, south to Monument Valley, then across NW and eastern New Mexico to the Texas Panhandle. Most days going out were 4-6 hours sightseeing, 100-200 miles travel. Coming back, 2-3 hours sightseeing 200-300 miles travel.
A couple years later, west along Route 66 to eastern New Mexico (about 300 miles in 3 days, a couple long stops), then diagonally SW through New Mexico to Alamogordo and White Sand, down to El Paso, across the Big Bend, then Davis Mountains and through Texas to Wichita Falls and the Wichita Mountains.
But it doesn't have to be a loop. We've been across I-10 going to Florida several times, making some stops eastbound while skipping others so as to make them stops on the westbound trip.
There are no universal "must see" places, unless you are trying to work through somebody's "500 places" check list. Everybody's interests are different. Find the places that interest you, connect the dots, look for other interesting places on the route, add those. Figure out how long you want to stay at each place, how long it takes getting place to place, compare that to your time constraints. When you find you don't have enough time, sacrifice your lowest priority stops, recalculate the time.
The really tough part is if you have too many places too far apart, as things can be very far apart in the west, compared to getting around in the eastern part of the country, or in Europe. The Colorado parks, Yellowstone, southern Utah parks, Grand Canyon can be done in 3-4 weeks as a one-way with really short (1 hour or so) park visits; tour companies do it, some with guest sleeping during the overnight drives, others with short airplane hops. But for a family doing its own driving, and driving from someplace distance, it takes careful planning.
One thing I've learned about RV driving is that it costs me at least 100 miles a day, compared to cars and motels, for the same amount of awake time, because of time needed to set up camp, prepare meals, break camp each day; this includes getting people moved around during conversions from travel mode to sleep mode. Another factor is wanting to be in a campground early enough to set up and enjoy the destination means stopping before or around the time of the evening meal, so no 6 AM to Midnight driving stretches like we used to do when trying to cover ground quickly to get somewhere. Four adults, all driving, however, you could possibly do 24-hour driving days if there was nothing along the way that you wanted to see.
