Where to stop between Yellowstone and Denver

We just made the drive from Colter Bay (granted this was Grand Teton's not Yellowstone) back home to Denver and drove straight through....we went out the east gate and 486 miles later we were home....took 287 all the way into Ft. Collins...beautiful country with multiple campgrounds along the way.

Southeast of Laramie, at exit 323, is the Lincoln Memorial Highway rest stop and it is a VERY nice one, large and quiet and fairly cool, etc. Great for an overnight stop.
Or go further east to Buford, a wide spot in the road that is a township, purchased recently by an individual.

Or, just south of I 80 on I 25, is the Flying J truck stop with a McDonalds with a BIG parking lot in the back.. Another good spot for an overnight.

Or, 7 miles south of Cheyenne is the Terry Bison RV Ranch.

Most of the suggestions so far are going to take you quite a bit out of your way.

Saratoga is nice, but it will take you off the quickest route (but the Saratoga route will be more scenic).

If you just want a spot on the way, and are going I25, I would suggest Glendo WY. There is a State Park there along the lake, and it is not far off I25. Guernsey is another State Park with camping. There is Register Rock (or cliff?) where the pioneers signed their names, and also some of the old wagon ruts from the Oregon Trail.

I can't think of anywhere that would be mid distance where you would really want to spend a lot of the day.

What gate do you plan to exit Yellowstone?

Saratoga Wy, a little farther than half way but nice area. You can go into Denver from the west or cut back to I80 to Cheyene and go south. Nice drive thru the mountains down to Denver. Just head south to I70 and then east.

The Black Hills may be about halfway, but will add miles to your total trip. Lots to see & do there. Salt Lake City, or the mountains in between/near there, is another possibility.

Lake De Smet near Buffalo WY has a nice CG on it. Closer to Y though.