Well shot, clever idea, and totally Japan.
Don't forget that in Japan "onsens" (public bathhouses) are a big part of the country's overall history & culture, up there with Mount Fuji & Sumo Wrestling. Most hotels will have an onsen of some description, and i'd dare say if you go to Japan and don't experience an onsen at least once during your stay you're missing out.
Beppu isn't exactly part of the main tourist hubs (Tokyo, Kyoto & Osaka), in fact as far as transport goes, you'll be putting your JR Rail Pass to good use just getting to Beppu (approx. 4 hours from Kyoto via Shinkansen / JR Rail) but something like this is a new forward-thinking way to get themselves on the map, which I think is worth commending.
Having said this, I still think if you want to really go full hog on your onsen experience, you travel up to Hakone or somewhere around the Fuji five lakes and grab yourself a nice Ryokan (traditional Japanese hotel) and perch yourself up there for a few nights. Great view, some excellent ryokans and you're only roughly 2 hours from Shinjuku Station via public transport.