I would like an Indy game along the structure of the Hitman games. It would be open ended that way it assures replay value. Marshall/Barnett College would be your "main menu" (think Lego Indy) where you're able to access options, missions, unlockables, etc. Marcus would be the guy to talk to if you want to access your missions. You could talk to students, staff etc to learn extra tidbits and hints as well.
Your adventure missions, like the hitman games, would be one large area with several ways to approach the objective. If you're raiding an ancient pyramid or tomb, there would be several ways in. You could be careless and set off all the booby traps, leading your presence being recognized by whatever tribe, or you could be careful and be in and out with the macguffin in hand. Or you could do a combination of both, and explore the areas perhaps to find more artifacts. There'd also be moments where you'd be able to be more "Indy" (like the options for Bond moments in the 007 games) where instead of jumping over a gap you use your whip, or you hit a guy with a chair instead of your fists. The same could go for infiltrating camps/ military bases. Then at the end you're ranked on what kind of adventurer you are. The more artifacts you find the more money you get in which you can use it to buy unlockables like different characters, production art, interviews, movie levels etc. You'd also get a higher rank if you finish the level with your fedora on.
To split up the adventure levels their would be driving/chase levels also, which would be a cross between regular driving games with minigames incorporated into them for the more cinematic elements.
That would be my dream indiana Jones game.
Dream on.