Based on last night's chat I came to understand that at least a couple of folks are seeing the tiles as sort-of Carcassonne-like, with pathways/tunnels and caves being different things.
As such I whipped up what I think is a basic set of tiles that covers the basic possible combinations. These aren't intended to be pretty, but rather conceptual. In a real game they'd be all squiggly and cave-like and all, of course.
Pathways/tunnels are gray, while caves are black. Any place that cave sides overlap are assumed to be one large cave piece that moves along both/all-three edges. If a pathway/tunnel enters a cave then that's good enough conceptually -- it doesn't matter where it enters the cave as far as I understand the game (movement is along full pathways or full caves, not tile-by-tile), so I didn't create every possible version.
NOTE that I didn't generate any that were pure-cave (no passageways) but for the final one. These can obviously be added if desired, but I got the impression that such tiles were undesireable as they're too likely to create a bunch of dead ends and/or be unusable.
You'll need to mentally rotate them to think of how they might interact. Each one has a number on it so we can refer to them by number in discussion.
The first set is pure passageways, with no cave edges. Number 1 is a dead-end (at Scurra's request):
Next are the tiles with one cave edge:
Then tiles with two cave edges:
Then the one with three cave edges:
Then the full cave tile:
If I missed any (and this was all done in a matter of 45 minutes or so, so I may well have) please let me know and I'll add them.
So... discuss. This isn't being presented as "how we should do it," but rather as a manifestation of what I heard yesterday.
Rather than editing I'll add another comment (in case anyone's replying while I type this).
I think this system is pretty workable. The total number of possible tiles is reasonably limited at 20. If movement was handled as something like one AP per passageway (any length, any number of turns, any number of crossroads) and one AP per cave (any size) then you've got a simple enough movement system to make it easy to calculate but a complex enough system that there's still some strategy to placement and movement.
I also realize that I forgot "standalone" caves, like these: