Its not what I'd call "open world" where your on an island and can freely go in any direction like Skyrim/Far Cry- the game is more or less linear with where it allows you to go, and the path you need to take to get there, but areas are generally wide enough to allow you off the critical path to find secrets and hidden areas , or just mess with the flora and fauna.
The game does give campfire "warp" points where you can fast travel to areas previously visited and come back with a new skill that allows to to reach something previously blocked.
Don't expect to be dumped in the middle of the island though like Far Cry, with freedom to basically go in any direction and mess around.
TR also has the " Fast Travel" feature which is very nice..lets you go to any save spot/ camp to look for items you missed on the 1st play through..it gives the game decent enough replay value too..some of the secret tombs are challenging to find, and there are many things to find in this game..I think it's more fun than FC3.
So is it a bit more like Dark Souls? Can you always go back to place at will? Or as the story progresses do the areas close off?
Not really like Dark Souls either, but closer to that than FC3. In Dark Souls, for instance, you could go to New Londo or the catacombs right away. In this game, there is a series of areas that are connected, but you get to them in a plot-defined order. You are mostly free to go back to areas you've cleared to explore though, so by the end of the game it's much closer to a free roam game because the while island is open at that point.