While we do not have a GUI method to do this, the API provides a list_neighbors function which you can run against a droplet. This will return details on any other droplets you own that are on the same physical hardware. This command can either be used within a program of your own, or via Curl.
You can also use the doctl command line client. Once you know the droplet’s ID number you can run this command:

./doctl compute droplet neighbors DROPLET_ID

Thanks for the response. I used the API and it indicated that neither of my servers have neighbors. Does that seem reasonable?