The Colorado experts might want to chime in as to when it isn't Monsoon season. I at least, know when that IS.
Hmmm, I'm surprised Lytehouse hasn't chimed in on this since she brought it up last night. Guess we are in though. I'm no expert, but since I end up planning a lot of CO trips for us, and most of my buddies for that matter, I'll go ahead and provide some input..
Weather...well normally July and August are monsoon season. 2014 was closer to a normal year and maybe even above normal as far as moisture (unfortunate for you Lee). Previous to that we were in a drought for years and the riding was great all summer, but not so great for homeowners with lawns because of watering restrictions, it was so dry. For road riding and lower elevation dirt (less than 10,000 ft), June can be a good month (early June can be risky). You can still get a freak storm, but they get pretty rare the deeper you go into the month. The high mountain dirt passes can be blocked till the middle or late June depending on the previous snow season, possibly even going into July for passes like Imogene/Black Bear/Pearl etc. Normally we do a lot of in state trips in Sept since the weather is pretty dependable for being great, except in 2013 when CO got hit with the 1000 yr floods in Sept which many of you may remember from the news. That was pretty much the beginning of our more normal moisture with one of the best ski seasons I've ever experienced and the return of summer monsoons in 2014. This latest cold snap put down some good snow in the high country for us hopeful skiers, but there is still a lot of winter left, so normal snowpack or not for 2015 is TBD. Normal monsoons usually means nice mornings, clouds building up around 1pm, rain between about 3-6pm, and clear skies when you are ready to cook out. End of the day, CO is an arid climate, the weather is not usually as wet as most places and all summer is great, just always have your raingear ready.
Location...SW CO is our favorite. Lots of great on and off road riding down there (Ouray, Silverton, Telluride area). Anything around Gunnison Crested Butte, Salida, Buena Vista would be another good choice for paved or dirt. Pretty much anyplace west of the front range is good for paved riding. I'm not as well versed on off-road riding along or north of Interstate 70.