Which eradicated viruses still have remaining stockpiles? Other than smallpox, I'm curious to know if there are any other stockpiles of eradicated or nearly eradicated viruses, and if so where are they located? Thank you.

Only two viruses have been eliminated in the wild to date: Smallpox (humans) and Rinderpeste (cattle). As the question notes, smallpox stocks still exist. So do Rinderpeste stocks; see Identifying and Reducing Remaining Stocks of Rinderpest Virus, which is from 2015, but has no indication that the stocks were to be destroyed in the near future.

The only virus that is "nearly eradicated" is poliovirus (human) and there are still many stocks of polio, although organizations are working on reducing their number ("Toward Eliminating Poliovirus—In the Lab).