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Looking for a route to drive to Yuma with mostly interstate highways & preferably thru South Dakota.  
Google was not much help so perhaps others on eBrandon will share their knowledge. Thanks.

Have done this trip before. Summary would be through: Rapid City-Denver-west through grand junction and south through Moab Utah-south through monuments ntl park to grand canyon then to Prescott AZ- then to Yuma.  
I would say that Moab was a highlight, awesome stuff there including Arches park. Prescott was a nice little town, cool twisting road south of there.  
Maybe not the interstate trip you planned, but we did this mostly on secondary highways on a weekend and it was a lovely trip! Making it west through mountains from Denver will depend on weather at this time of year, well it might all depend on weather.

Do you just want the quickest? Mapquest.com shows two possible routes. One of them goes further west and would be more scenic but I wouldn't choose that route in the higher elevations in the winter. The other one goes south on 85 along the very west side of the Dakotas to Denver, south through Moab to Phoenix then west to Yuma. I added a screen shot.  
 
Edited by bigmoe, 2022-01-11 07:19:07

you mentioned a screen shot for the route but I didn't see it

If you are on the phone app open the photos tab.

If you want as much interstate as possible your best bet is likely to take I94 to Bozeman, MT, then US191/US20 to Idaho Falls, ID. From there it's I15 all the way to Las Vegas. Then US95 from Vegas to Yuma. But that doesn't take you though SD.  
 
Best bet if you want to go through SD is to get to Spearfish, SD, then head west on I90 to Gilette, WY. From there take I25 to Casper, WY, then south on US287 to Rawlings, WY. Next head west on I80 to Salt Lake City where you meet up with I15 following the same route as above.

We went down to north platte, Nebraska and spent the night. Then down to Albuquerque, New Mexico and spent the night. And then to Phoenix.  
Was ten hours, ten hours, six hours. That was in November, not sure if another route is better in January.

I did that run a couple of times on my Goldwing. The only advise I can give is not to do the Denver route in winter. Snow squall's and closed highways are possible. I would go through Salt Lake City and then down.  
 
Another recommendations would be, pick a hotel chain that you like and follow the route that has those hotels. I am a loyal Best Western guest. Just google Best Western locations in the States you're going to pass through and make your route according to where the hotels are. I picked Best Western because they give point that add up for free stays and have gift card promotions every once in a while.