Hmm... Here's my idea.
Typhoon
Basically, they only occur between the start of June, and the end of October. It's a huge wind and rain event. More on that later. A day before the Typhoon hits, they'll be a message on the message board about it. The neighbors will discuss it, and if you talk to Kapp'n, he'll say that his services will be cancelled for tomorrow, due to the Typhoon.
The day of the Typhoon, controlling around will be different. For starters, going against the wind will slow you down, while going with the wind makes you faster than usual, but will also cause you to trip. Neighbors will also be in their houses all day, and most of the time, they'll talk about the Typhoon. Getting stuff from trees will prove to be impossible, as they'll be whipped away by the wind. Doing mayoral work with Isabelle is cancelled, and Nook won't upgrade your house/change the exterior. In fact, his inventory for today will be empty. Club LOL will also be closed for the night. You can go inside, but Shrunk will say that tonight's show is cancelled, due to said Typhoon. You can still go to Brewsters, but you'll be unable to do any work for him. And special visitors won't come that day. And no campers, either. You can attempt to dive, but you'll be prompted that it be a bad idea to do so during the storm. TVs, and the Antique Radio and Cabana Wall Radio will only pick up static. And sometimes, the lights inside the houses will flicker a bit. (You won't go through a full-blown power failure, don't worry.)
The day after, you'll have to do some clean-up. Some trees will be knocked down, almost like they were chopped down. You'll have to get rid of the downed tree with your axe, which is the only time your villager will use its axe in a downwards chopping motion. If you break an axe, Leif will give you a new one. Speaking of Leif, he'll be around for the cleanup effort. Help him clean up, and you'll be rewarded from Leif. The cleanup can last up to a day, but Main Street will be pretty much back to normal.
So, what do you think?