It depends I believe.
When you bring Site and Item as dimensions, duplication does not matter.
I think you have measure value as well and tried to pick up one , but without full scope of your task, it's quite difficult to suggest.
Please attach your set of data as twbx format.
I you just drag only the 2 columns in the rows shelf in tableau it will automatically show the grouped data. i.e removing the duplicates showing the values only once.
Incase if you use any other dimension along with this it may just expand as per the different values the dimension has in sites and Item.
What I'd like to do is count the total number of time each item is selected, but only count it once for each site. Any ideas on how to do it?
We still need to see your data.
Please Please Please attach twbx and clarify your expectation.