The Andy Griffith Show, but I don't know about the adjective "weirdly." The show is supposed to be cozy and comfortable, and it succeeds better than any other show I know. Hilarious, too. Barney Fife is the funniest character in the history of TV. I even named my Lemmy handle after him.

Perhaps a better choice would be one of my favorite Star Trek series - Next Generation, Deep Space Nine, or Voyager. I record them on TIVO, so I have a huge bank to choose from. I often watch an episode as the last thing before going to bed.