A few ideas for you all kind of ideas that i have had but not and several flavors of trips that range in length;
Arkansas river - maybe put together a multi day pseudo camp/chill starting as high as the numbers and going to BV, Salida, or on through the royal gorge. I have thought about trying this but haven't so others may have better beta on that trip. No permits needed, but fees for campgrounds could rack up.
Upper Animas- It's awesome and big in my opinion. Absolutely beautiful trip. I don't think you need a permit for this as a private trip.
Dolores river - if we get lots more snow in the San Juans and the dam does a release, though it can be tough to get accurate info from McPhee Dam. Lots of options if you can hit the timing. You can decide how long you want it to be, starting at bradfield bridge you could go all the way to Moab, or on through cataract. Or San Miguel to Dolores to Colorado river from telluride to Moab.
Piedra river - 2 day trip that's pretty far from Denver and SLC
Gore canyon- classic
Roaring fork - multi day is possible though camping could be tough to find
Did you explore the yampa already?
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