Onsen visit in Hakone or Kyoto?

The water temp at an onsen is generally pretty hot for a child that age, so he/she is unlikely to spend much time in the water. Day trips are an option, and you'll have to check with the inn if they permit day visitors: some do, some don't.

There are lots of onsen that aren't associated with overnight lodgings at all, and then of course a day visit is the norm.

This is an option that would appeal to everybody, I think:

http://www.yunessun.com/english/

It's huge, and has a waterpark area, themed baths that the family can enjoy together (everybody wears a bathing suit), and finally a really nice traditional (well, as traditional as can be in this setting) onsen area called Mori No Yu.

You and your husband could take turns experiencing the onsen part of the day while the other one hangs out with your five year old.

Very do-able as a day trip---just don't miss the last bus back to the train station (at Odawara, I believe).

Many ryokan have onsen hours that are open to the public. You can find these in any onsen town, at least the kind that don't require bathing suits and are gender segregated (which are the majority).

I have seen little kids in onsen baths enjoying themselves - in a rotemburo that is more like a hot outdoor pool.

There are a few places in Kyoto that advertise as having hot springs. You can find them listed here with the red hot water icon:
http://japaneseguesthouses.com/db/kyoto/index.htm
But you can see from the fotos that the baths are nothing like Yunessun.

Arima Onsen is an onsen town not too far from Kyoto and might have what you are looking for.

Children are welcome and a common site at all ryokan in Japan. Remember the baths are a Japanese ritual and are practiced by all in Japan. I have never seen a cleaner people. Some kids love it and I have seen some who don't like the hot water much. Most ryokan will have a family bath either indoors or outdoors where you can hang a sign or lock the door and have a private bath situation. You can even reserve a time slot ahead of time usually done when you check in.

Aloha!

I like the idea of stopping at Yunessun. My kid would be very pleased with that place! I understood from the japan-guide website that we can take the Hakone Tozan mountain tram and hop off at a station and then take a taxi to the onsen. What is the best way to get back? Are there buses to Odawara, in which case we can take the shinkasen from Odawara back to Tokyo. How much time should we plan for the whole trip?

If we don't head to Hakone while in Tokyo then I think Arima would be a good choice. Is it easy to get to Arima from Kyoto?

Thanks.

Really loved the Funaoka Onsen in Kyoto.Would recommend it.Among the oldest,has a gender seperate baths.A great place to unwind & refresh before dinner.Kids are allowed.The only thing is the adults around are absloutely naked-thats if it is of concern to you or your hushand taking the child in.
Funaoka Onsen,Sembon Imadegawa kado, Murosaki no Minami, Funaoka-cho, Kita-ku, Kyoto.