If you are going for the cherry blossoms and get the opportunity, take the Shinkansen up to Aomori Prefecture and go the Hirosaki Castle. The actual Cherry Blossom Festival isn't until late April but it's still an amazing place to visit. I was stationed in Aomori Prefecture for 3+ years and there is an incredible amount uncommon tourist stuff to see there. Lake Towada is a lake formed by a huge volcanic blast that is ringed by hotels, onsens, and walking paths and was very cheap to visit. Cape Shiryazaki is a section of beautiful coast with wild horses, cliffs/unique rock formations, and a light house. It honestly looks like it belongs in Ireland, not Japan. While driving to these places there are cool little roadside produce stands and shrines everywhere. When I first got stationed in Japan I was really bummed that I wasn't in Tokyo but when I left I couldn't have imagined having been anywhere else other than Aomori.