In Utah, stop at Arches and Canyonlands National parks.

The Arcj is definitely worth a look. Fsscinating.
If you are in SLC when the Mormon Tabernacle Choir is practicing it is an experience I will never forget. I don't know how admission is done now (this was a long time ago), but I believe it was a Thursday night.
Lawrence has an Indian School museum.
I think I'd look at the map for your Denver-Cheyenne-SLC portion. That doesn't seem to compute correctly to me.
From Denver drive I70 west and see the hot springs in Glenwood Springs, and also the part of I70 in that area. Astounding.

I hope that you are aware that this time of year weather can be an issue..esp at Denver. Make sure you have chains, pack blankets & other safety equipment and be prepared to delay travels if weather & road conditions warrent for safety...

Depending on the type of car & your road expereince, I would consider going south and up the coast of California I-5: even the Grapevine pass on I-5 can have some early snow/ice and fog issues.

From Denver to Salt Lake, I-70 is much more scenic than I-80 west of Cheyenne. Both roads may be subject to adverse weather, but I'd say that I-70 would be a better bet because of the efforts to keep this road open for skiers. The key to your trip will be flexibility. Any storm, in the mountains or on the plains, can be dangerous and should be avoided. You'll need to keep up to date with the forecasts and warnings and be prepared to lay over a night or two somewhere when necessary if the roads are closed. Hopefully, bad weather won't be an issue for you.

If you do take I-70, there are some great places for short stops. You can do a quick drive-by tour of Denver, the State Capitol, City Hall, Art Museum, etc. in a few minutes! Then drive west and see Red Rocks Amphitheatre, off I-70 in Morrison - it's a Denver City Park open free of charge year-round. Astounding views. Further west is the old mining town of Georgetown, worth a quick look. Then you'll go through the Eisenhower Tunnel at the Continental Divide and into Summit County where some of the major ski areas are, then past Vail which would be a nice stop. The next area is Glenwood Canyon and the town of Glenwood Springs - if the timing is right, it's a great overnight stop so you can enjoy the huge natural hot springs pool. Then you start to get into a more high desert terrain, through Grand Junction and over the border into Utah. Arches and Canyonlands National Parks are less than an hour's drive south of the interstate and I'd highly recommend a detour if you're in the area. Unforgettable scenery. Then take Hwy 6 northwest through Price to get to I-15 and Salt Lake.

Best of luck with your planning and your move!

I concur with tekwriter. That is a good route. If interested, I can give you a cut off route through western Colorado and take you into Salt Lake via US 40. It is much shorter if passing through Salt Lake BUT very weather dependent. Second, forget the chains. We have lived in the Denver area for nearly 30 and have never owned a set of chains. BECAUSE -- if it is bad enough for you to need chains, then you ought not to be on the road in the first place. However, having quick access to winter clothing, some food, and water is not a bad idea in the unlikely event that you get caught somewhere. The weather and roads in the mountains are fine the vast majority of the time so the probability of a problem is low but it happens. Keeping an eye on the weather is critical. The newer policy in Colorado is to close interstates fairly quickly so that a lot of cars and truck are not trapped on the interstates when it turns bad. Signage and road information is very good in the mountains.