Grew up on the other side of the mountains and about an hour from Gunnison.
What everyone else said, pack warm clothes. I've watched 4th of July fireworks in a snowstorm, Colorado altitude can be temperamental.
As far as a route, If I were doing it I would go through southern Utah and end up in Durango, cut north to Montrose on the Million-Dollar Hwy. (550), over to Gunnison and then on the way out go over Monarch to Salida, north out of there on 285 through Buena-Vista. From there you can cut over Independence through Aspen, or go up through Leadville and take battle mountian past red cliff to minturn. From there I would cut back on 70 and go through Moab, and get back on the route you came back on.
Just remember August in Colorado will be stop and go traffic pretty much everywhere, especially around Aspen/I-70. Not "fairly busy, slow going", Independence pass on a weekend in August you probably won't get over 10-20mph. Stop and go.
I can tell you some places that won't have traffic and are beautiful roads to ride, but they are very out of the way, and aren't very "touristy", but still in my opinion some of the most beautiful spots. (See: Naturita/Uravan/Gateway/Grand Junction, or Salida/ Cotopaxi/Westcliffe/Walsenburg/Alamosa.)
Westcliffe, CO born and raised so I know the area fairly well.