For TOS, I'd suggest "The Tholian Web": a clever, tense story that deftly brings out the heart of the Kirk/Spock/McCoy dynamic. Plus, it's got cool aliens and some of the better FX work.
Also, what with the Space Madness and Scotty dashing off to get crocked on Klingon nerve gas, it allows you to inoculate your new viewer against the cheesier elements of TOS. If your viewer doesn't enjoy that stuff and take it in stride, TOS just may not be for them.
For TNG, I think one of the more high-minded standalone episodes, like "Darmok", "The Inner Light", or "First Contact", would work well, since they highlight TNG's differences from TOS.