Take a look at https://www.skyscanner.com. They have a "cheapest month" feature. All you have to do is choose your destination.

To see it, choose your flight then in the date pop-up choose Whole Month -> Cheapest Month.

I believe they also have the inverse where you can choose a month and a departure city and they'll give you destinations by price. I couldn't find it quickly though but I think they have it.