This was sent to Chris via pm, but I thought I would go ahead and post it up here to bump the thread, and in case there is anyone else looking for the info...
Good morning Chris, I think I can help you out....
Normally June is peak of our snowmelt, and when the rivers around here are highest, but this year is looking to be the driest in a decade. If things keep going with the current weather pattern, we will likely be looking at small peaks on all the Colorado drainages earlier than normal (probably early May), and they will be at either low levels, or a few places will have dam release.
The Colorado River from Burns to Dotsero would be a good option. Class I with a few II's, good camping and scenery, as well as multiple access points.
The Arkansas would have a couple options, but they are all going to be in the II+ realm, the first stretch there I would look at is Big Bend to Salida.
Another option would be the Wagon Wheel Gap stretch of the Rio Grande (from below Creede to South Fork), or from South fork to Del Norte.
There is one stretch of the South Fork South Platte where beginners start (Deckers, aka Chutes). It is pretty much solid II, with one easy III, but all roadside.
There are a few other options that are a little farther away from you, including the Colorado River near Grand Junction. The Gunnison above the confluence with the Colorado. Lower East River. Lower Taylor (at low water). Lake Fork Gunnison Box (II-II+, but beginner friendly), and the Animas above Durango (Baker's Bridge).
Oh, a couple more include the Eagle River below Wolcott and Grizzly Creek to Glenwood Springs on the Colorado.
There isn't much in the central Mountains on the difficulty level your looking for, too much rock, and too much gradient.
Hope that helps.