Now there's a sign you don't see every day:
裸で階段の昇降は固くて断ります。

Climbing the stairs while naked is strictly forbidden.

So where can you see it? Why, at Dogo Onsen (道後温泉), Japan's possibly oldest and certainly most famous hot spring, located only a few kilometers from the center of Matsuyama, in the prefecture of Ehime on the western coast of Shikoku. (Interestingly enough, the literal meaning of dôgô is "end of the road".) With a recorded history of over 3000 years (!), Dogo has admirably resisted the urges to modernize and hike its prices into the stratosphere; instead, it has a vast array of different prices and different services for different budgets.

So. Simple no-frills entry into the Kami-no-Yu (神の湯, "Bath of the Gods") costs a mere ¥300, but that's all you get, you even have to bring your own towel and soap. For another ¥320 -- the level I picked -- you're loaned a yukata and fed green tea and a few sembei cookies after your bath. The entrance process for this second level is a little on the confusing side though: you have to ascend the stairs and disrobe right there in the relaxation room, in sight of all the attendants and anybody in the street below who's looking up. But only down to your underwear -- after putting on your yukata, you go downstairs, strip away the last vestiges of your dignity, and enter the bath. (There are coin lockers if you need to store your valuables, at ¥100 a pop.) The bath isn't particularly spectacular, just two identical giant granite tubs in separate rooms, more often than not full of Japanese tourists. It was almost at capacity on an off-season Tuesday (albeit just before dinner, the most popular time to bathe), the place must be a sardine can on holiday weekends.

The process repeats in reverse on the way back (and you'll see the above sign at the bottom of the staircase), except that you can lounge about in your yukata for an hour, sip on the tea (free refills) and maybe sample a range of other, surprisingly affordable snacks and drinks, all in the ¥100 range. (Try the local specialty, Botchan dango, which are tasty little multicolored balls of mochi on a stick.) The relaxation room is on a breezy 2nd-floor balcony, nice and cool even on a sweltering summer day and with nice views of the yukata-clad tourists clip-clopping about the streets. The entire place is surprisingly traditional with few concessions to modernity, eg. not a vending machine in sight.

Should you want to get away from the unwashed masses, you can fork out another ¥360 -- we're up to ¥980 now -- and enter the Tama-no-Yu (玉の湯, "Bath of the Spirits"). Tea and cookies are provided here as well, and you finally get to borrow a towel too. And if you cough up yet another ¥300, you can retire to a private room on the 3rd floor for changing and sipping tea for all of one hour and twenty minutes.

Still not satisfied? Then you can book Botchan's Room, named after the protagonist of Natsume Soseki's famed novel of the same name, who used to lounge around the place when off duty (as Soseki did in real life). Prices are negotiable, but presumably not terribly cheap. And for even more luxury there's the Yushinden (又神殿?), reserved for the use of the Imperial Family and so hallowed that a mere glimpse inside will set you back ¥210.

Compared to many of Japan's other extravagant onsens the facilities at Dogo are really on the simple side, so if you want waterfalls and jacuzzis you'd best look elsewhere. However, for sheer depth of history (and a pretty nice traditional building) I think Dogo is well worth a visit if you're in town. In the off-season I'd suggest the Kami-no-Yu with the 2nd floor cookie deal, but if it looks really packed I'd probably spring the extra few hundred for the Tama-no-Yu.

A minor source of confusion is that these days "Dogo Onsen" refers not only to the original bath house, but the entire surrounding little town of hot spring hotels and their accompanying restaurants, shopping streets, nightspots, etc. But aside from the bathhouse there is very little to see in the vicinity, although nearby Isaniwa Shrine (伊佐邇波神社) may be worth a peek and Matsuyama Youth Hostel is an excellent place to stay.

References

http://www.dogo-onsen.co.jp
Personal experience