Check out https://en.wikipedia.org/wiki/List_of_map_projections

But since this is probably going to be a fictional map, I'd just put on a square grid/hexes that will be used for calculating movement without the projection

If you want to have a hole in the ground, check out https://en.wikipedia.org/wiki/Contour_line#Elevation_and_depth
Adding lines themselves might be tricky. I think I would rather open the map in GIMP and modify the colour of the area with a mask layer. I guess there should exist some map software where you could just "click and carve" but I haven't heard of it

I've got a nice thin one under my office chairs, and I could see that. A little thick for my taste, though.

Although I can see drawing the grid directly onto one, and then playing on the other side. Then you could even put illustrated maps underneath projecting the grid onto anything.

That's definitely a whole project though. Onto the pile it goes.

Out of the box: we wanted a transparent plastic covering for a cheap IKEA cabinet that we sometimes eat on and wanted to wipe more easily. The solution was a clear vinyl mat designed to live under office chairs to protect the floor. We cut to size with a box cutter. Works great. Probably would work for you.

I assume you replied to a notification, that doesn't reply to the comment, it puts it on the main post. I've made that mistake a few times.

I've been looking for a good one, but I'm having a hard time finding any coating or film that presents itself as the obvious best choice. Most of the options I've found have mixed reviews.

Nice, thanks

I don't use hex personally but in my opinion Tiled is very good. And since most of its files (tilesets for example) are XML, after you figure out how those are created, you can automate creation of new ones

Also, maybe this will be helpful for your use-case

Very nice! Add a plastic film on top for easy wet or dry erase markers and this is mint.

I made a hex map with Sharpie on a 3'x3' piece of white hardboard. Took forever since you have to draw every edge individually, can't just do entire rows like a square grid. I enjoyed it though, and I was able to add some details to help my players adjust to hex distances.

Markers on a blank grid. Works great in Linux. ;)