With casting Indiana Jones, he has to be an actor who you could buy as an archaeology professor and a daring action hero who can kick butt in a fight. This is one reason why the casting of Harrison Ford was so genius.
If they were to recast him as a young man, I'd like to see them get someone who is not a big star but someone who has enough experience under his belt to be able to carry a big movie as a leading man.
A couple of actors I've thought about:
Josh Duhamel: He's probably most famous for his role in the first 3 Transformers movies but he's been in a variety of different movies. He is in his 40's now though.
Liam Hemsworth: His brother Chris was attached to Spielberg's Robopocalypse project. Liam is only 23 so he would be a very young Indy.
He's played several American roles so pulling off the accent wouldn't be a problem with him.
James Marsden: He's most famous for being Cyclops on X-Men but he has proven a well rounded actor doing comedy, drama and action. He's also got that cocky persona that you want for Indy.