Some of my favorite fishing is on the Platte, between Six mile gap and a campground called Pickaroon, (where the Douglas joins the Platte.) Only access is by foot, and has had very strick slot limits and bait regs for several years. Flies and lures only. Not exactly near Laramie, but is accessed through Albany, over the Medicine Bows, and down to the Platte. Closer to Laramie, I still get a kick out of beaver ponds for Brookies. There's a lake called North Crow Reservoir between Laramie and Cheyenne that is left alone in the spring for the most part.
Next week I'm heading to some "warmer water" around LaGrange and Torrington to try some spring cat's and eyes!