"What is your favourite thing to do in an Animal Crossing game?"
It's hard to say. I like fishing in the older games, especially if there's chance for a coelacanth -- it's the best way to make Bells in a pinch. Since New Leaf has the island, fishing is less useful, so for that game, I'd say going on tours is the most fun. Tours are a very unique challenge, and if you're playing with others, they're even more fun.