Lots of places to hike in to. I'd suggest either the Rawah Wilderness Area or RMNP.
Flies, spinners, grubs... Trout eat everything, just gotta find what they want.
I suggest UL gear because its easy to pack in and more fun on the troutskis.
Use the search function on here for specific info. Use google maps to find bodies of water and then do some research on them.
Colorado is great for backpacking in to a location and trout fishing. You can look at RMNP near Estes for lakes with good brookie and cutthroat action. Better scenery than anything you have in Nebraska, but probably won't get into any giants.