I did a similar route 6 or 7 years ago and like others have said, there are lots of options. My route was:
US285 South to Fairplay, then take Weston Pass over toward Leadville/BV. Tons of camping on both sides of Weston, although the west side has incredible views of Massive and Elbert.
Head down from their toward Mt Princeton, and then take Tincup Pass. The nice thing about Tincup is that you get two nice ghost towns on either end of the pass with Tincup and St Elmo. Good for a stop to walk around. You can also take a dip in the hot springs. Tincup can be late to open because of a snowdrift near the top of the east side, but I'm thinking that late July should be safe.
On the other side of Tincup you are in the Taylor Park area, which opens up a huge amount of possibilities. You can pop out and head to Crested Butte on the highway, or take another detour up Taylor Pass or Italian. Like Wes said, those routes have more snow and you may need to monitor into the summer to see what opens up.
1976 FJ40 - green and mostly stock
1996 FZJ80 - not so stock