Judging by the age of the vehicle and using the national miles per year average (12,000) that Envoy should be around 84,000 miles. Being a 4x4, you will want to make sure the trans/transfer case are in good working order. UV joints and rear axle should be free of leaks. Replacement of these will cost thousands. Of course there is the gas mileage issue and how much it takes to fill the tank.
Generally speaking when purchasing a used vehicle with high miles your going to be running into a host of problems. If you purchase from a dealer, you will want to invest in some type of warranty offer. If your purchasing from a private seller, you will be on the hook for all repairs the minute you sign that sale contract. Private sellers are not responsible for anything once you purchase it from them. Hence the buyer be beware slogan.
Any vehicle can last for 200,000 miles if it is well maintained and cared for. You will want to get as much information as you can about the previous owners use of the vehicle. Like did they tow a boat with it or was it a daily driver or was it only used on Sunday for church. Check GMC's website for recall information. Ask people who own them what they think.
I was in the same boat as you a couple months ago. I wanted a large SUV but I didn't want high mileage or high payments. Ultimately, I drove a couple different SUVs (Envoy, Durango, Tahoe, Yukon). Each had it's pluses and minus'. For me the Envoy was not powerful enough, the Durango was too small inside and the Yukon was too expensive. My situation is a bit different than most, I don't drive alot. I have a company car so the Tahoe I bought was strictly for recreation. So getting gas for me is about every 6 weeks.
Good luck, hope this helps.