Laramie is home to the only university in Wyoming (University of Wyoming--UW, or "U-Dub" as the locals call it). The town itself is around 28,000 population. I would think that the job opportunities there would be fairly limited. The cities with the biggest law office presence are Jackson (hideously overpriced resort that culturally really isn't even part of Wyoming), Casper (the state's trade center and home to much of the "oil patch" business community), and Cheyenne (the state capital). Both Cheyenne and Casper have populations of only around 50-60,000 each. The whole state population is only just over 500,000. Rents are very much dependent upon where you locate--reasonable in some places, unreasonable (if anything can be found to rent) in others.
My personal guess for best chances for work in the legal field would probably be in Cheyenne. Know, too, that there is a relatively strong prejudice in favor of hiring UW graduates in many workplaces. Where I worked for several years, I was one of the few graduates of a college other than UW in a relatively large operation--but I was in a relatively specialized field where there were few qualified Wyoming individuals. I would absolutely recommend that you have a job lined up here before relocating.
If you are a middle-aged single guy moving to Wyoming, there is a good possibility that you will stay that way. There are a lot of very nice women in Wyoming--nearly all happily married. It is not a "singles scene" kind of place. (Denver is probably the closest place with that scene, but most Denver women I know would never think of living in Wyoming.)
One other thing about the culture. Many people think that because Wyoming is very politically conservative that it is a "Bible Belt" kind of place. It's not. It very much has retained some of the attitudes of the "Old West." Things like alcohol and guns (hopefully not together very often) are very much still part of the Wyoming culture, just as hard work, self-reliance, honesty, and straight-forward dealing are.
Finally, if you haven't lived outside of the South, you better check out the climate in Wyoming. While it's not as harsh as some might lead you to believe, it is not for the faint-hearted. Go to
Weatherbase and check out the averages for Wyoming cities. Laramie, in particular, is at around 7,200 feet and has relatively long and rigorous winters. I'm not a good person to comment on the climate because I'm a Rocky Mountain region native--this is the climate I know and love, but it's not for everybody.