The Upper Rio Grande
Its hard to beat Southern Colorado for variety.
I would second David's advice on Gunnison.
But if it were me, I would setup a campsite somewhere above Creede (maybe even above the Rio Grande Reservoir). There are lots of great tributaries to fish on the Upper Rio Grande, if you are willing to do a bit of hiking. A very under rated fishery....
If you want to stay in a hotel/motel, Durango would be another good choice. Lots of fishing options within an hours drive, without as much hiking.
Also, another overlooked stream is the Conejos River. Lots of great fishing and in a beautiful location. Camping and Lodging options abound. Lots of good tributary streams, as well.
Best time of year would be Mid/Late July to Mid/Late September...
"Even a fish wouldn't get into trouble if he kept his mouth shut."