My first activity that I would like to do on the Apple TV is download some of the great new games, including: Rayman Adventures, Beat Sports, and Oceanhorn.
I'm sure as soon as I connect it, my kids will be begging to play Minecraft so their wish shall come first. After that, I'll probably scroll through the menu so I can get familiar, since I've never owned an Apple TV.
My first thing to do with the new Apple TV would be a movie marathon!! I have a lot of movies I got for cheap by buying digital copy slips that I've been saving up, the new Apple TV would be the perfect device and excuse to watch them.