After playing around a bit with Blender I was able to find a solution to the issue and I'm posting this here so it can help others too:
What you want to do is to make the external model(the main map) separate from the internal model(the cave) then go into Unity and put the model in. When you click on the model in Unity it will show you where the missing pieces are.
Using this as a reference, go back into Blender and delete the faces that are causing issues, then add more vertices and faces, save it, then go into Unity.
Delete the current model from Unity then re-import it(clicking re-import doesn't work for some reason) and check again in the model view. If you fixed it, you should be able to see the missing faces are covered either partially or completely. Keep doing this until your model no longer has any missing faces.
As for the cave or internal model, go into edit mode and press ctrl+shift+N to bring up the normals menu and simply check the box that says "inside".
This will make the faces visible on the inside of the model. Once you do that, just put the internal model inside the external, add a few faces, vertices and edged to connect them, flip them the right way and you're done :)
I hope this helps people as I was pretty stumped with this for a while :)