Japanese school year starts on April. Usually, public schools are off on last week of March and first week of April, kids usually have two weeks off. Because of this tourist places can be busy on April 1 and 2 due to kids are out of school. Also end of March and beginning of April is cherry blossom season and there are large number of non-Japanese tourists will be visiting Japan. With these considered, hotels will likely be slightly higher in rate.

If you are looking for onsen (hot spring) area, since you mentioned Hakone, there are Kusatsu onsen, Kinugawa onsen, Izu peninsula, are all overnight destinations. Using shinkansen, overnight trip to Tohoku area is also possibility form Tokyo with a lot of Onsen.

If not Onsen, Matsushima near Sendai is a nice area. Because of Shinkansen, Kanazawa is now easy overnight destination from Tokyo. Karuizawa and Nikko are other overnight destination form Tokyo. Kiyosato in Yamanashi are mountain resort area, Kiyosato may be less frequented by non-Japanese compared to other locations I have mentioned.