I graduated UW and left Laramie in the mid 2010's, but I really enjoyed my time in Laramie. Vedauwoo climbing was fantastic, but the winters can be extremely harsh. There is more population than just the students, but being a relatively smaller town, there is the feeling that the population gets recycled every year. This also means that the local crowd tends to be close knit and makes for strong friendships. I have never lived in Lander, but spend a fair amount of time there. The winters can also be extreme, but you will likely have more climbable days per year as Sinks Canyon is a great cold weather crag. There is the NOLS and Christian College in Lander, which also compose a major portion of the younger population and may make it feel a little cliquey. Hunting, ranching, and farming are also a major part of the lifestyle here, more so than in Laramie. Lander is a little more removed from larger cities, which may factor into things like air travel, concerts, road trips, etc. (as opposed to FoCo & Denver being just down the road from Laramie). I would all in all say Laramie is more youthful and progressive, but the people are more transient, while Lander is a little more home town conservative with a more close knit local crowd. Obviously there are great people in both, and that is just my experience!
Lander is right at the foot of the Wind Rivers for great backpacking and alpine climbing, and is a good hub to other portions of the state (there is much tribal land here as well that is restricted). Laramie has a small ski hill less than an hour away, and has access to gorgeous yet smaller mountains in the state (snowies and laramie range)
Either one, be prepared for getting snowed in for days at a time, as late as March or April, with snow shutting down the highways.