There're tons of places like that.

Just in lower Hakone areas alone, there are these:
http://www.hakoneyuryo.jp/price/
http://www.yumotofujiya.jp/dayplan/plan/bath/index.html
http://www.fujiyahotel.jp/dayplan/pl...spa/index.html

In Arima Onsen (near Kobe), there's this:
http://www.arima-gh.jp/facility/family.html

Anyways, there're many other places.

Sorry these are all in Jpnese and I don't have time right now to translate the details. But there're certain restrictions such as the time of the day that the hotel ones are available to day users, as well as different packages. If any of these interest you, then let us know if you have questions and I can provide info when I check back.