No expert on Wyoming but maybe around Alcova Reservoir (south of town), or west a little bit towards the Rattlesnake Hills. Wyoming has a LOT of unoccupied acreage, so finding a boondocking site shouldn't be too hard. Have a great trip!
If you can go out a bit, consider Vedauwoo outside of Laramie. Neat rocks, and a choice between an established campground or two and oodles of boondocking spots.
__________________ "If a man does not have an ideal and try to live up to it, then he becomes a mean, base and sordid creature, no matter how successful." Letter to his son Kermit, quoted in Theodore Roosevelt by Joseph Bucklin Bishop, 1915