I don't understand why all this types of applications assume that a have a destination and dates. I'm very flexible and I can work remotely. Surprise me with the cheapest flight anywhere. Does this kind of app exist?
Discover Destinations does that. You input what kind of destinations your looking for (food, hiking, museums, etc.), and it'll show you the cheapest flights.
If you put a start airport into Skyscanner, you can tell it that your destination is anywhere, but you still have to pick a date. But it's a decent way of seeing where you can fly to cheaply.
Once you pick a destination, Google Flights lets you bring up a monthly view so that you can see which days are cheapest to fly (and sort/filter by things like flight time and price).
Google Flights also has explore functionality (IIRC, red dots are airports you can reach directly, grey dots are not), but it can be a bit hit and miss.
This is a co-worker's project that seems to match what you want
Birmingham, Alabama, GB (BHX)