There is so much to love about the CT that it is hard to narrow it down just one part. Some of the most beautiful scenery IMO comes after San Luis Peak-- Spring Creek, Carson Saddle, Molas Pass etc and depending on the time of year you was thinking of for your trip, then this is where I would go.
If you are looking at earlier in the season, then the Collegiate Range could provide some interest in and around the Twin Lakes and then make your way towards US-50 or Marshall's Pass. Here you also have opportunities to climb a few 14ers (Mt. Elbert, Oxford, Yale, Harvard and Princeton) should you wish to side-track. Note, this area could see a little more traffic.
I also recommend the La Garita Wilderness area starting at Eddiesville TH. In fact my wife, father-in-law and myself come here at least once a year to hike and fly-fish; it is a beautiful part of the country.