I went Wednesday this year. Great trip. Flew to Atlanta, stayed in Madison and drove into Augusta early.
Some tips:
Don't rent from Hertz: They are notorious for overselling major events at their Atlanta facility. I was "guaranteed" a midsize and they had....nothing. Told me it would be a three hour wait. I was able to make other arrangements but it was really stressful.
Get your hotel room early. Like, NOW. We stayed in the Hampton Inn on the Interstate in Madison Ga and then went in, saw the old homes (Sherman spared Madison) and had a beer in the old town square and went to a cool restaurant down the street and sat outside on the deck overlooking a park.
http://www.town220.com/ We had a blast. (Hampton Inn was just adequate, not great, but great location. Madison has some great old B&B's but they were full).
I hear Athens the night before is a great way to do it as well.
Get up early and get yourself to Augusta. The traffic sucks and practice rounds end early on Wednesday due to the par 3 tournament. You want to get there early enough to watch the players at the range and then follow some folks around the course (practice rounds are very casual with people hitting multiple balls so sometimes you are better off moving on to the next guy).
There are some interesting back roads that parallel the interstate on the way to Augusta if you feel adventurous. (We had to use them to get around a wreck, beautiful countryside but cost us 20 mins).
Walk as much of the course as you can. Try to see someone skip the ball across the hazard to the green on No. 16. I even did a cheesy "walk up 18" (in that case with Angel Cabrera) just so I could relive it when I watched it on TV that Sunday. The finish this year sucked but it was so cool to watch the tournament and say "Cool, I just walked there."
Don't be shy about checking out the members in the fenced off umbrella patio. Getting to see Arnie from 30 feet eating lunch in his green jacket was very cool. You see a lot of other celeb types too.
Find a nice spot on the first fairway or first hole of the par 3 tournament. It's the closest you'll get to so many pros, and to see them with their families dressed as "caddies" is fun.
Eat at least two pimento cheese sandwiches. At least. And pay the extra buck for the better beer because it comes in a better souvenir cup that survives the dishwasher better.
PM me with any questions.