If you want all the dots to be exactly the same size and exactly the same distance apart, and if you want final say over how the edges of the subject matter are portrayed, the best way to do this is the tedious way. Dot by dot. haha
But it's not as bad as it sounds because you can create large amounts of dots in seconds if you're using paths, right? Whether in Photoshop or Illustrator I would:
Drag in my map as reference
Make a new layer
Put a circle path on it at the size I want
Copy/paste enough dots to make a row wide enough to cover the whole map
Duplicate enough rows to cover map vertically
Delete the ones you don't need
Then you have a fully editable layer of dots from a less destructive workflow.