It's hard to imagine, but there are over 50 lakes in the Eagle Cap Wilderness, many of them with good populations of Rainbow and Brook Trout. The hard part, of course, is hike it requires to get there. The area with the greatest concentration of open water is the Lakes Basin. It's central and reachable from almost all the trail heads in the area with the Lostine River/Two Pan Trail Head providing the closest (and most popular) access. Fishing is an awesome experience in this absolutely gorgeous area.
Because of the compressed season, these fish can be pretty fickle about if and when their ready to bite. Towards the latter part of July, fishing for Brookie's can be very lively as these fish get ready to spawn in the aquatic vegetation just offshore- but once that spawning begins it's like someone hit a switch and… nothing.
Fishing the small streams is another fun challenge, as you discover that these fish are acutely aware of things approaching their vicinity above water. Sneaking a fly onto the water without being seen becomes the name of the game.