My ideal Indy game would be more of a blend between Emperor's Tomb and the Thief series, wherein you can switch between 1st and 3rd person. I liked Infernal Machine, as it had some massive, fantastically-made levels, but it was essentially a Tomb Raider game gameplay-wise, and I think Indy games should go in a different direction. The Emperor's Tomb combat conveys how combat in an Indy game should be (limited ammo, lots of fist-fighting, etc), so that should stay. However, Emperor outside of the combat had nothing more than linear platforming which infests Tomb Raider (and Uncharted, I think). Platforming should be at a minimum in Indy games . . .the guy is an archaeologist, not a circus performer or an acrobat. I have no problem with using the whip to get across crevices, etc, but climbing up crap and shimmying along ledges has been done to death already in other games. Instead, I suggest sprawling, non-linear maps filled with enemies, booby traps, and puzzles a la the Thief series. I want to get lost in a vast ruined underground lost temple, dammit, hearing and fleeing echoes of shouting, angry Nazis down one of the dark passages behind me. I want to be able to sneak past those Nazis rather than having to kill of em.
One of the issues with the Emperor's Tomb combat is that guns just don't do enough damage. Indy can take a spray of submachine gun fire and still be standing. Of course, if guns were realistically good and not a "ranged alternative" as seen in Emperor's Tomb, no one would ever use their fists. That's why an Indy game should be more of a stealth game than a platform game--you have a rationale for why Indy is fist-fighting.