Getting around downtown will be extremely difficult since 108,000 people will all be trying to get to the game. You might find a parking space in a garage depending on what time you go, which would have to be early in the day since the game starts at 4. People start the partying pretty early down here and downtown gets crowded quickly. Also, forget trying to have dinner after the game that night because all of the people coming back to their cars will stay downtown for dinner.
You will have to pay the highest parking rates they ever charge. I don't remember what those rates are now because I don't go downtown on game days anymore! Someone else may know. Last year, the garage I was trying to get into to park just to go to the library, that one was $10.
Downtown traffic patterns are altered, streets blocked off, etc., so you might end up lost accidentally and on a street where you don't know how to get back around to where you wanted to be. It has happened to just about everyone I know at some point.
Sorry to be the bearer of bad news... I know that this post sounds really negative, but I'd rather be straight with you about what you're up against. You can definitely still visit downtown, and during the time the game is on, it might be nice and quiet... you just have to get in and out while the Vols are on the field, and overall it will not be an easy task.