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.

Your host has a responsibility to make your schedule in such a way that it will be full and engaging.

Sometimes, it can be difficult to fill the schedule - it requires that people respond to the hosts invitations to meet with you. Your input can be helpful both in filling out the schedule and making sure that your visit is productive.

You can request to meet with specific people and ask for feedback from your host on who you might want to speak to.

I think it would be a good idea to request to meet with graduate students in addition to postdocs and senior scientists.