Going East/North is cooler in summer.
Karuizawa is a favourite summer retreat and should be nice scenery for someone from Singapore. I stayed for a few hours and left because it just looks like Canada!
Sendai/Matsushima also scenic and should be OK in summer.
Above accessible with JR East pass. Also hotels are significantly cheaper outside of Tokyo. 8000yen double rooms (not ryokan) in business hotels readily available, if booked early enough.