Backcountry climbing ideas in CO/WY/MT?

Hey folks, I'm East Coast-based and looking to combine some backpacking and climbing somewhere in the high Rockies, thinking a week soemtime in late summer (late Aug - mid Sep).  Ideally, we'd want to put together a backpacking trip of 4-6 days that could take us to some climbing spots you wouldn't get access to in the course of a regular day hike.  I and my partner are comfortable on sport (up to 11bish) and trad routes (up to lower 10s), open to single or multipitch.  Any thoughts on places we should check out?  I've done plenty of alpine backpacking in the CA Sierras, and climbing in various locations, but haven't done either in CO/WY/MT... Thanks for any suggestions!

Wind River Range would probably be exactly what you're looking for in Wyoming. For the better backcountry rock in Colorado, most of it is possible to do in a day, but some more "backcountry" options could be Lone Eagle Peak, Crestone Needle, Vestal Peak. RMNP is awesome and you can certainly bivy there too, but it's not as much a backpacking destination unless you go to some of the more obscure stuff.

I've not done any alpine climbing in Wyoming but in general, it seems like much higher quality and more plentiful than what we have in Colorado, with the exception of RMNP and parts of the Indian Peaks Wilderness. The problem with those areas can be getting permits & like Jon said, the climbing areas are not always the best backpacking areas. If you are interested in the Indian Peaks, Lone Eagle Peak North Face is a great backpack as well as a great climb with variations that remove a lot of the hiking / 3rd class scrambling. You can do it in a day but it is worthy of an overnight. Plus, it's not a far drive from Denver and flights are plentiful.

The Winds seem like the move, especially if you can get a direct flight to J Hole or even SLC.  I would start with Steph Abegg's site for her amazing topos and TRs.
However, if you don't mind a long drive or an expensive flight (Durango) and "variable" rock quality, go to the San Juans in CO. No permits needed and the backpacking is awesome.
Grenadier Range: North Ridge on Arrow + Wham Ridge on Vestal makes a good weekend from the same campsite. You could add on the Trinity Traverse if you want to do some scrambling. Or, head deeper and do the North Face of Storm King.
Pine River: The Pope's Nose is on my bucket list, it's just a long approach hike. If you break up the hike, combine it with some lines on Tradistan Tower and Vallecito Crag, you could get the best of all worlds.

Wind River Range without a doubt.