As an undergrad at UT, I can confirm that bikes are popular. I do not bike, because the campus is quite hilly ("The Hill", for one) and I'm just not a biker. There are motorized scooters and such, which I imagine would be ideal. As for the roads outside of campus, they are not mountainous. I use I-40 almost exclusively to get everywhere I want to go and, as you can imagine, it's like any other interstate. With the exception of the revamping of the downtown area this summer, traffic is not a problem - at least not anything like it is in Nashville. If you're at all familiar with I-24 through Nashville, you know it's riddled with construction (and has been for several years) and the main highways and thoroughfares are quite unmanageable. This is not the case at all in Knoxville. Aside from the obvious rush hour traffic, I've never had any issues. This goes for downtown and the old city too, which is preferable to that of Nashville, in my mind.
Also, while summers are absolutely warm and the winters cold, it does not snow with any regularity at all. In fact, longtime residents have told me they do not recall ever having snow days during school. This winter, it snowed maybe twice, with little to no accumulation, and was melted by midday. The idea that it snows often here is a misconception. I do find the weather pleasant nearly all the time, as we often have a strong breeze from the mountains that cools hot days and pushes storms out quickly.
As far as living goes, I wouldn't say you'd be completely set with simply a bike. Do you plan on living very close to campus? While certainly affordable, these places are often the most expensive and the least desirable in and around Knoxville - at least for someone intending to make a life outside of the undergrad scene. Places like Fort Sanders come to mind, which has recently experienced a rash of crime, although I would still make note that Knoxville is quite safe on the whole.
I live about 5 minutes from campus near Alcoa. The traffic is never bad and you can find homes for very reasonable prices in the area. Places on the west side of town are considerably further away and nicer on the whole. As a non-biker, I can't imagine riding from my home or from anywhere else but right on campus, although I admittedly don't know how far people who bike normally travel. Public transportation is more than adequate, as I have friends similarly distant from campus who regularly take KAT (Knoxville Area Transport) and don't have problems. The university also operates a robust bus system.
Not sure if you're still interested, but it may be helpful to others.
