I had a map just kike that.
TEMPLATE
I made a wooden hex template, 3 inches big, with lil nail-heads underneath.Then I used the template to cut out hexes from 3" wide foam board strip with a razor blade (not responsible for severed fingers). Did I forget to mention, I mounted a handle on the template - makes grabbing easier.I cut different thickness of different colors and had interchangeable hexes. I could shuffle my map all up. Trick is to make your wooden template PERFECTLY hexagonal in shape, it must be perfect perfect perfect.
HEXES
I cut 3 inch wide (must be precise, consistant 3" width) strips of foamboard to use this on. Cut different thicknesses and different colors to make interchangeable hexes. Each hex will have a blank white back side, that you can draw custom terrain things like rubble, obstacles, etc.
BASE:
Get styrofoam panels from Manards, Cut it as wide as you want, and long as you want. (foamboard warps - avoid that for a base). Assemble a bunch of hexes onto it, and straighten them up. Now build a lip around them with something.
I painted my styrofoam underneath blue. So when I wanted water, I just left an open hex.
MAPS:
You can stick a few of these down with long tacks into the strofoam underneath. They will still be a bit loose no matter how well you cut them. You may want to fiddle with them until you get them as you like, then glue them or pin them down, or put plexiglass over it. ut I hate plexiglass, I like to be able to shove pins into the map as I need to mark things.
I had to give mine up. I kept them all loose and interchangeable with a few pinned down. But semi-feral cats seem to take great joy into wedging them up and all over the place.