Good morning.
First of all, how many days do you plan to stay in each city? As you probably know, staying in Izu or Hakone and going sightseeing in Tokyo would be quite tiring. Because of the distance.
Hot springs are not often found in big cities, but are found a little further away. And the accommodation you want is relatively easy to find in Izu or Hakone. However, if the room has a bath with a hot spring, the accommodation fee will be quite high.
There are also accommodations that do not have a bath in the room but have a private hot spring in the facility.
Next is Osaka, but there is Arima Onsen in the neighboring Hyogo prefecture. It takes 45 minutes to an hour by car to get to Osaka. There are also hot spring accommodations in Hiroshima if you go a little away from the center.
Of course, there are hotels with hot spring baths in all of these cities.
However, if you want accommodations with a hot spring in the room or a private hot spring, I recommend staying in a hot spring area away from big cities such as Izu, Hakone, and Arima.
I am a qualified tour coordinator.
If you wish, I can suggest and book a facility that will fulfill your wishes. Of course, you can also book transportation and various activities.
I hope your journey is a good one.
Regards.
Tak