With it being HC weekend, no such thing as too early. Get there early and grab some breakfast at Rama Jama's and enjoy the parade which I think starts at noon? With late games, if I'm not tailgating, I'll normally head over to the Strip and grab some lunch at one of the restaurants there because you can usually find a table that points to a TV with the afternoon game(s) showing. A mexican place on University across from Publix called El Rincon Bar and Grill is my favorite, but Little Italy in the shopping center on the other side of the street is good too. Buffalo Phil's is also a good spot.
For parking, closer to the Quad/stadium you can pay a little more to the boy scouts and park, but have more difficulty leaving (traffic), or park a little further away at Central HS on 15th St for 10 bucks and have a little longer walk but less congestion leaving.
Other than the Bryant Museum, which will be packed of course, just take in the sights and sounds of the Quad. Explore the campus. Chances are you will run into someone you know at some point for you walk around for a while, which is really cool if that person is tailgating... Check out the band pep rally in front of the library on the Quad and/or the Walk of Champions at the Stadium... and most importantly, meet up with Doemasters... he will lead you to the action!