Satellite parking exists in areas but I don't think anyone can guarantee what will be available next season quite yet. The traffic is crazy after games, there's no way around it. You won't be stuck forever but you won't get out in 15 minutes without a little planning - and also flat out leaving in the middle of the fourth quarter. If you're just there to take it in, and don't give a hoot about staying to the clock hits zero .... eh ... just leave early. Best thing you can do to help yourself if you want an easy exit.
If you want to do a good home game next year, you're either looking at Oklahoma or Georgia. Oklahoma will be a revenge game for the visiting team, and Georgia could potentially be a "top 10 vs top 10" kind of showdown. Oklahoma will likely come sooner (ha) in the schedule, and Georgia usually comes later in the schedule - usually - so in all honesty I would just prepare your wallet for the Georgia game if I were you. You don't technically need a second mortgage to get tickets to UT-UGA - but it'll help.
The area outside the stadium is fun, but packed, before the game. Your best bet will be to get the schedule for the band, stroll around a bit, catch the Vol Walk, follow the band in, and next thing you know, kickoff. If it does end up being a big showdown, it'll either be a 3:30 or 7:30 kickoff, so that'll give you time to drive down, park, and check out the scenery.