I had to laugh at the suggestions that you come to Italy just to visit Gardaland. Yes, Lake Garda and the surrounding area is lovely and, if you have your own transport, it is possible to make day trips to see other interesting, beautiful places like Verona and Venice.
But I really don't think Gardaland (or any of the several other theme-parks clustered near it) merits a trip to Italy. Italians - most of whom never leave Italy when on vacation - think they're fantastic, but if you're in the USA and you want a theme-park vacation, it will be cheaper and you'll have a much better time if you go to one in Orlando, Los Angeles, etc. If you're in Britain, go to Alton Towers or Disneyland Paris; apart from the almost guaranteed sun, Gardaland has nothing on those places.
Asking "What to do in Italy?" is not much different to asking "What to do in the USA?" The answer to that could be: visit the Grand Canyon, see the autumn colour in New England, visit the original Disneyland, see Manhattan from the top of the Empire State Building, go whale watching off the Alaskan coast, wander around a county fair in Iowa or get a tan on Miami beach. Similarly, the answer to someone asking "What to do in Britain?" could be to visit the Tower of London, go hiking in the Lake District, go surfing off the coast of Cornwall or take a tour of the Scottish Highlands.
Italy is a big country and there's lots to see and do, but sensible advice depends on knowing the sort of things you want to do, how much time you'll have and when you'll be visiting.