I presume this is true of all of us, but I am a big fan of golf courses where one can tumble off a green and onto the next tee. I think having an extended pause and a walk between one hole and the next dissipates a sense of continuity and intimacy that my favorite course routings seem to have.
That's why it makes no sense to me to place the next tee box 40 yards away when it could be 5 or 10 yards away, especially if that tee box will be on the back side of the previous green. The risk of getting hit by a shot from the group behind doesn't strike me as a big one, since golfers overwhelmingly miss short of pin-high, and it takes incredibly little effort to just be alert to players on the nearby hole while teeing off.
Naturally, there are environmental and terrain-based hindrances to doing this on a lot of sites, but I've seen countless holes where there didn't appear to be an excuse other than the architect not taking the extra time to get players from green to tee in minimal steps.
Among classic courses I've played, Pine Needles does a great job with this (especially since it crosses a couple roads), as does Secession on the modern side.
Having looked on Google Maps, it looks like Old Elm in Chicago would be a contender for the title, as would Friars Head.
What (other) courses out there have the shortest total green-to-tee distance? Bonus points if the 1st tee and 18th green are super-close to the clubhouse patio.