Option 1: Find somewhere to go within our budget, no matter where it is.
To do this, we go to Skyscanner, put our departure city, and select "everywhere" under arrival city and "cheapest month" under dates. This is how we booked a $480 round trip flight from Mexico City to Rome (direct and virtually unheard of) in December 2017, when we weren't planning to go to Europe, but ended up visiting five countries while on the trip. The same happened when we were living in Seoul and found a flight for less than $200 to Vietnam during our limited travel dates. We didn't initially have a particular desire to go there (it was simply the cheapest option), but it ended up being one of our favorite trips to this day.
Option 2: Find a flight to the specific destination we want to visit, but only when it's cheapest.
For this, we'll already have the destination in mind, but are only willing to travel there when the flight is most affordable. We track prices using Google Flights, which is how we found our Tokyo flight at about $540 and our flight to New Delhi for $450, both out of LAX. Even though we were living in Mexico City at the time, we flew out of LAX for these flights because it was much cheaper. Flying to LAX from Mexico City cost about $180 each at the time, which we were prepared to pay as it still would have been cheaper than flying directly out of Mexico City. We did a Google Flights scan at the same time to make sure flights to LAX would be cheap around the time of both of the trips, and they were.
Typically, when you book a flight this way, you may have to travel during a "less desirable" time (like Europe in the winter). But, we lucked out and were in Japan during the Cherry Blossom season. And, in Europe, we got to see the Christmas Markets, so aside from the cold weather, it was worth it.