I'm planning on doing that race rapwithtom mentioned, and possibly have to travel during the week, but want to ride on the 2nd weekend, more if I'm able to get out of work. If it was my thing to (selfishly) plan I would plan Copper Triangle on 6/25 and you should stay in the front range on 6/26 and do a ride in the plains/foothills, and not train out until Monday. I ride C.T. on the July 4th weekend every year, so that would mean doing it two weeks in a row, but it's such a gem, I wouldn't mind. Would have to be flexible around weather though, you can get bad days in June in the mountains.
Copper Triangle in Copper Mountain, CO, United States | MapMyRide
You can do it from breck but it really doesn't need to be any harder
Copper Triangle from Breck in Breckenridge, CO, United States | MapMyRide
One thing, it's better to leave the mountains on Saturday afternoon than Sunday, traffic can be crazy bad. Although Saturday is no guarantee either.