When I was there, you could walk around to the front entrance into the Masters and get your picture taken on that mound with the flowers in the shape of the U.S. (see picture below). No charge for it (of course). Not sure if they still do that or not? But that's worthwhile if the line isn't too long.
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I will also say... walking the course could take it's toll on some people if you're not in the best shape. It wasn't an issue for me, but it was a bit for one of the guys. This course is WAY more hilly than it looks on TV. The #5 fairway, I'm pretty sure it was... has a crazy slope from one side of the fairway to the other, and a HUGE fairway bunker. And walking up 18 is literally a hike.
Like I said before though... after my wedding day and the birth of my two children, this might have been the most enjoyable day of my life. It's everything you could imagine it being and more. The golf shop alone is UNREAL. Just soak it all in and enjoy.
I keep trying every single year to get tickets and win the lottery.