Is it appropriate to bring some kind of gift for a host professor?
I'll tackle the easiest side of the question first: bringing nothing should not create trouble. If you are clearly expressing your thanks for the invitation, both in written before you arrive, and in person when you meet the guy, noöne should take offense.

On the other hand, bringing a gift is fine too, but:


It should be tasteful and suitable for any taste: no sake, no unusual (by US standards) food… unless you know him well enough.
It should not be terribly expensive: people like the attention, but they don't actually care so much about the gift itself. Keep it simple, that way it cannot be understood as a bribe.
Not academia-related, but still useful to remember: make sure it passes customs (I had my French gift confiscated from me once).


I usually bring stuff to colleagues who host me when I travel to other places, if only because it gives a starting topic for smalltalk (something which I'm not very good at) in a future occasion.