Stan:
You mentioned you want to come out to Wyoming in the spring. Remember spring comes a little later in Wyoming than in the mid-west. Especially, if you plan to hike to high mountain lakes as some of these waters only become accessible in late June or early July.
If you enter Wyoming via Interstate 90 the nearest trout fishing is just across the border at Sand Creek (public fishing a few miles south of I90). Further west are the Bighorn Mtns. that offer a variety of angling opportunities. Alpine lakes and reservoirs; some that require a hike to access. Mostly smaller streams, some that can be good to excellent fishing.
Some notable streams would be the North Tongue in the northern part of the Bighorn National Forest and the Middle Fork of the Powder River that is west of Kaycee on BLM lands.
Depending on if and how far you want to hike there are numerous alpine lakes and reservoirs that contain a variety of fish including Yellowstone and Snake river Cutthroats, grayling, rainbow, brown, lake and brook trout.
Do some homework, make some calls and you should have a good trip.
Buffalo Fishhead