Any place where there is not a great deal of pressure on the fish will be a great place to go and you will have better chances at landing one, or several. the key is–the farther you get away from civilization, the fewer people will be willing to go there and as such, the fish will be more naive and willing to bite. Being an avid fisherman, I might suggest a couple of things. Find a high basin lake away from roads where the people will really have to work to get there. Google maps satellite images–this is the main tool I use when scouting for hunting areas and fishing spots. Sometimes I hit pay dirt, sometimes I get a dried up lake-bed. The San Juans are great for fishing, and scenery. That is where I would concentrate my efforts. And, while I am at it–if I am driving all the way to Colorado to fish, I am going to call Nate B at Animas Valley Anglers. I took my daughter fishing on the San Juan River below Navajo lake in NM (just south of Durango) and we were covered up in trout scales. Like I said, if you are going to spend the money to go to Colorado, hire a guide. The cost is about $4-500 for a day of fishing for 2 people (tip is customarily 20%) And you are using the guides river-boat and expertise. That makes up for a lot of frustration if you are not catching anything. It is one thing to hike and sit on a lakeshore and “plunk” waiting for the trout to bite, a complete separate experience to go and target fish. I know I deviated from your OP, yet if you are specifically going to fish, you might need to plan accordingly. You’ll definitely want to pinch your barbs to make catch and release easier on the fish (and use artificial flies.)
Off trail, Haviland Lake and Electra Lake are great places to fish for dinner. The lake trout in Electra lake are second to NONE. Think Salmon.
Stephen / Birdog