The academy is located on the top left corner of your island. You will first rebuild it during the questline. I cant remember the exact level I was when I got that quest, but it was probably around level 5. After it has rebuild you will need to upgrade it once, which will cost 40,000 coins. The academy enables you to upgrade the attacks from your dragons. With a level 2 academy, you can upgrade attacks to level 2. You can save money early on to upgrade the academy, but I advise to advance a little further in the questline first, and build other buildings like farms and habitats.