So much choice my head is exploding so hoping to get some personal recommendations!

One night stay in Hakone end of November
Family of 4 (children aged 8&11)
Onsen is a must - probably private or easy to book privately as husband and I both have small tattoos
Location is fairly important, we'd like to do the rope bridge and the open air sculpture park but also have to be at Narita for our 5pm flight so I've read we should be on our way by midday at the latest. We'll be coming from Kyoto
Traditional ryorkan with dinner and breakfast (prob with western breakfast option for the kids)
Budget: I can see Hakone is not cheap! I'd like to keep it under $400 if we can

Thanks Fodorites!