There is a user here on the site whom I'd like to contact about something entirely unrelated to Drupal - he lives in/near my hometown. Is there a private message system or an email system? I looked on his profile but could not find anything.
Whenever somebody writes a comment below any of your questions or answers, you get the typical SE-notification about that. Not "private", and not by "Email", but better then nothing. Know however that "delete comment" means actually "hide from anybody except moderators". And if YOU want to allow anybody to eMail you (for similar questions), you can just mention your own eMail ID on your profile page (using the typical work arounds to not make it too easy for spambots to grab that eMail ID of course ...). Variation: suggest some URL where people can contact you (eg via D.O, or another website).– Pierre.VriensApr 17, 2017 at 12:17
Stack Exchange doesn't provide any way to contact user privately, except via a chat room you create, where the only users who can enter are the other user and you. (The chat room needs to be set like that, or it will be accessible from every user.)
Keep in mind that chat moderators can always enter rooms to which other users don't have access.
Alternatively, if they show their email in their profile, you can contact them using that.