Now that I'm replaying the game, some of the criticism is coming back to me. For instance; I liked how you had the Tombs that you could discover, but don't really like how they're implemented. It's too optional. It's precisely what I think Siegfried77 said - the game feels IMO too much like surviving the island, rather than "tomb raiding".
What I would like to see is a game that is more like the original Tomb Raider. Discover some distant from civilization disconnected place, discover a Tomb, that leads to some mythical device etc. In that sense, I want the tombs to be bigger, much more central to the entire game and story, rather than the disconnected "mini tombs with mini puzzles" that we got in this game.
In the original Tomb Raider, you got 4 locations if my mind serves me correct:
Peru, Greece, Egypt and Atlantis.
What I found most enjoyable about the original game was that you got to traverse, explore and discover 4 totally different locations with very different architecture, type of puzzles, natural enemies. The adventuring and exploring mythical places defined the enjoyment of the game.
If you effectively limit the locations to one single one, I am concerned that you will end up traversing various places multiple times, limiting the variety and exploration of the game.
Exploration was always the series biggest advantage IMO. Where Uncharted is a mix of story driven 3rd person shooter with a bit of adventuring conveyed through the different locations, Tomb Raider should be exploring (perhaps more openly), less but more effective combat (less enemies, but perhaps more challenging ones) ones.
As an example; In the original Tomb Raider - progressing deeper and deeper into the tomb at Peru... you really got a sense you're in some magical place filled with traps and puzzles. If you actually tried to reach the more hidden less accessible caves within the cave, you came across Dinosaurs (and that encounter with the T-Rex) which was totally WOW. Totally optional, but one of the most memorable parts in gaming. It's a pitty the 2013 Tomb Raider is totally absent from moments like these. I really hope it's something they can change with the sequel.