Okay, you got me with the "Let's" example...but just to play devil's advocate, I would still argue that "check out" is an expression that is fine in normal (and informal) speech, sounds very US (and therefore familiar!) to me, but that in a formal setting you would use looking into (as in, maybe, an email to a colleague you don't know at work: "My assistant is looking into airfares..." ("checking out" seems a bit too casual for me in this last example.
But when you put "let's" in front, it makes "look into" seem more natural and widely used. So I guess, after all this chatter, what I mean to say is that it's more a question of where "check out" sounds appropriate, because "look into" sounds pretty good everywhere.
Thanks for the heads up, Chaucer, I need to be more clear on which of the two expressions is more versatile in tone!