JAPAN Sengoku Jidai - places to visit in May?

[oliver.japan]

I apologize in advance if this is a bit off topic on a Miniatures Forum, but I thought I would ask anyway given the level of expertise and passion of many people here ... 

I will be travelling to Japan for work in May. 
Any particular places you would recommend visiting, in connection with History in general, and Sengoku Jidai more specifically?
I will be staying in Tokyo, but during 3 weekends I will be free to travel around the country if anywhere is worth a specific visit.
Beyond "just" museums and castle, I would also be interested in live Re-enactment festivals (I went to Shingen-ko matsuri in Kofu years ago, was amazing!), or even theme parks (like Jidai Movies Studio Parks) as long as these are not just tourist traps.

PS: I already visited Himeji, Osaka and Matsumoto castles
PPS: I lived in Japan a while ago and still speak fairly well, so I am not limited to "Gaijin-friendly" english-speaking locations. 

Many thanks for the kind tips, and again, apologies if this is off topic here.