What's the etiquette for a short visit to a US university department by a faculty member from another university?
I think you are the person who would be invited out to lunch, dinner etc. as you are the guest :) ! However, there is nothing wrong with inviting your opposite number to talk in an informal setting. The only consideration is that you know the lay of the land! 

Depending on how many days you would be spending at the US university, you might want to make a strategy on conversations and prospective collaborations. 

I am assuming you would have results to show and tell and with a punchline at that. That generally helps.