I am an undergrad at UT right now and I love Knoxville. Knoxville is really affordable! You can find apartments for about 4/500 dollars that are in a good area and pretty large. I always think of the Heights when I think about affordable living in Knoxville. It is about a 5 minute drive to campus. Also if you wanted to live in walking distance it would be really easy to find something close to campus. It would probably cost around 600/700 for a nicer apartment near campus. There are some that are really cheap, but I would not really recommend living in some of them. Typically if you are looking in the fort I would say that staying closer to Cumberland is better/safer/nicer. Also there are a lot of great restaurants in Knoxville! You can make 18-22K work in Knoxville while having plenty of money to go out to eat and go to concerts and bars.
The weather in Knoxville is pretty great. We usually get about one snow day a year and it is because we get like 3 inches of snow. Most of the winter is above freezing. Also during the spring and fall you will want to spend all of your time outside. We are close to some great places to hike and explore. The summer can get a bit hot.
Also the faculty are great! They are always willing to take time out of their day to talk to me about applying to grad school, so I would imagine that they would be even more willing to help their graduate students. Also I know that we have a lot of people who do research on education, econometrics, and health. There is also the Boyd Center for Economic Research and the Baker Center for Public Policy that do a lot of economic research that grad students help with. Also the placements at UT have been going up over the past few years.
I would be happy to answer any other questions you have about UT!