My plan is to be there when the gates open and walk right to the first tee and go walk the entire course before it crowds up.
I would recommend walking it backward. With plenty of stops to look back to see what the "shot" looks like, of course.
Then I'm really not sure. I hope to eat a lot of those cheap sandwiches and drink a lot of lemonade's. Then I'll go buy some presents for my wife who was instrumental in making this happen.
Do the bag check. They'll store it for you so you don't have to carry it around. Or just mail it all home. Very easy.
Also, the rule on saved seats is that you can sit in them, you just have to give them up when their owner returns (duh).
Any suggestions on things not to miss? I've heard there are monuments and plaques out there. I have no idea what they are or where they are, but I'd like to go hunt for those too.
As an amusing side game, try to find animals: birds, chipmunks, squirrels. Good luck! There aren't even that many insects (like bees around the flowers). Try to find the one palm tree on the grounds (if you don't already know where it is). The only hint I'll give you is that it's on the right-hand side somewhere.
Have fun!