Family friendly onsen for day use near Tokyo

Hello,

I have lived in Tokyo in past for many years and plan to visit in March next year with family of 4 (2 girls 7 & 10 years old). I can speak some Japanese and am comfortable to navigate train/buses etc. I will be staying close to Shinagawa Stn.

We would like to spend a day at Onsen, preferably that has something more than just a bath (like dine inside and do some walking around post bath). We have been to Yunessun in Hakone and it was fun for kids but this time want to do something more traditional.

I was thinking of below options, Please give your thoughts and add other options that I have missed. Ideally I would like to stick to US $350-400 for the whole family including transportation & meals (flexible to spend more for a better experience)

1. Atami - Its proximity to Tokyo is great. I dont know any onsen that would allow day use for family so any recommendation is appreciated. Also any recommendation on activities post onsen in the evening also appreciated.

2. Other areas close to Tokyo (Izu, Hakone) where above is possible with a day trip. Any recommendation on onsen?

3. If I expand the area outside of Kanto, Does it makes sense to do day trip to let say Gunma or somewhere else within 60-90 mins train trip?

4. I once did a packed trip through JR to Minakami with 1 night stay at Ryokan and it was an amazing trip, However we didn't had kids at that time so it was still budget friendly. If I want to stay one night at Ryokan with kids, how much approx would it cost including tickets, stay and meals in March 2024?

Thanks a lot
KB

I recommend you Kaneyamaen Ryokan , near mount Fuji,here u will get onsen experience