Of course, the earlier in the day you get there - the better chance of a parking place near the stadium.
BUT - in case you cannot get there early enough (after having driven aroudn a little to SEE what's got spots here or there) - you can try doing the trolley thing. You park your car in downtown Tuscaloosa anywhere - near the AmSouth bank is one idea or even closer, if you like (like near the University CLub, for example) - & let the trolley pick you up on one of its (every 30-minutes) runs - it will deposit you on campus & you can go on to the stadium then or just enjoy being on campus until time to go into the stadium. The trolley takes you back to your car afterwards too.
By coming early enough , though , you should be able to find some place either near the Ferguson Center or near the new little shops across from the strip (near the new Publix) or over near the colesium or quad. Good luck - it's always a fun day no matter WHAT!!!!