I lived in Paducah for a little while but left because it had very few opportunities. It is pretty far away from any larger cities and the local job market leaves a lot to be desired. If you're looking for a well-paying job or colleges, you will find little here. While the real estate here looks affordable, that's because the crime rate is much above the state average and there are few high-end jobs available.
On the other hand, Paducah has some nice natural areas you can visit. Shawnee National Forest sits along the cities northern edge and is a great place to visit. You can hike there or just visit for an afternoon with your dog or some friends. There aren't many stores here either, so you'll need your own car to drive to neighboring cities to find what you need in a lot of cases. If you have an opportunity to live somewhere else, you're most likely better off taking it.