A lot depends on what you want to see... Presuming, since you're going to Yellowstone, that nature/extraordinary views would be toward the top of your list.
I'd suggest taking US 40 EAST through Hot Sulphur Springs and on to Granby. Right off the bat, there's Hot Sulphur Springs if you'd like to stop and soak for a bit.
If not, on to Granby. There, you could detour up US 36 to Grand Lake and take in the sights there. Plenty of camping areas around Grand Lake. Notable is the Timber Creek CG inside RMNP. All first come/first served, so no reservations needed. If you have a towed, you could also go up into RMNP. If you don't, you'd be hard pressed to find places to pull over and see the sites with a class C. There's a car rental place in Granby, perhaps consider that for a tour into RMNP without the C. You'll enjoy it a lot more that way, trust me!
Going back to Granby, take CO 125 to Walden CO. Up and over Willow Creek Pass, barely noticeable by CO pass standards. Take your time from the top of the pass into Walden. Depending on the time of day, there's a good possibility of moose sightings along CO 125.
From Walden, continue north on CO 125, which becomes WY 230 when you cross the state line. At Riverside, it bcomes WY 130, which takes you north to Saratoga Springs. Again...a great place for a soak in the hot springs there. Take a walk around the downtown, funky little shops in town.
WY 230 up to I-80 then west to US 287 north to the Grand Teton/Yellowstone area. Other folks can chime in with things to see/do on that leg. But you can certainly take more than a few days just getting out of Colorado!
