We have a wii u upstairs, and just recently bought one for the basement. We have several downloaded versions on the upstairs box already, specifically Mario Kart 8. Are we able to play that game in the basement as well, without paying full price for it again? (I wish now that just purchased the hard copy as that could have been transferred between consoles when needed.)
No, you can't have one nintendo ID registered to multiple consoles.
Once a Nintendo Network ID has been associated to a Wii U, it can only be used with that same Wii U. There is not currently an option within the system that will allow you to transfer the Nintendo Network account from one Wii U to another.
They do have a support link to do that sort of transfer on the site, but I doubt they would be willing to go back and forth multiple times.