My 2 cents:
1. Get there as early as possible. Would aim to be in the parking lot an hour before gates open due to traffic on roads and foot traffic at gates
2. Personally, I would head to the picture spot in front of the clubhouse and get that out of the way. There are at least three lines to this, so should move quickly early in the morning. It's a free picture, so don't want to miss out.
3. Would then meander to the pro shop. I would have a premade list of items to purchase. It can be overwhelming in there - it's like the size of a walmart lol. There are two pro shops. one by number one fairway and one behind 16. 16 may be less crowded, but it's further away so thinking coming from the picture area you should stop at the main pro shop off 1. They can ship everything for you so if you don't want to lug purchases around you don't have to.
4. After that I would venture to the concessions right by the pro shop. Would snag a blue moon or their local beer. It's funny they are so anti-brand there that they don't list what beers they are. You just choose domestic or import or craft. pretty sure the craft is blue moon though (and you get a green cup instead of the clear one.)
5. Try every sandwich and ice cream there. Will set you back about $20 for all of that.
6. Walk the course and take as many photographs as you can. Would try to recreate some famous pictures you've seen for a personal/office shadowbox or scrapbook.
7. Wear the most comfortable pair of tennis shoes you have. Those puppies are going to be barking after you get home. A picture can't do it justice how downhill like the 10 tee box to 10 green is.
8. I don't think gopro's are okay. could be completely wrong, but I think it has to be a still camera.
9. Post the pictures in here so we can be jealous
As far as things to do in Augusta, if you are into bourbon, they have a distillery called 2nd City and you can do a tour and buy some of their goods. They also have started doing a Masters themed single barrel bourbon named after each of the holes at ANGC. This is their 3rd year doing it. Cool collectors item.
Enjoy!