Himeji Castle is the the one everyone thinks of when you say "Japanese castle", although it postdates the Sengoku Jidai. It's the one in the Shogun TV series that stands in for Osaka castle. Well worth the visit; should be doable in a day from Osaka.
A couple of days in Kyoto will get you castles, temples, and a trip to the older districts like Gion will let you see some traditional houses and streets. Very atmospheric, especially in the evening, and you'll probably catch sight of a geisha or two. Don't wink at them like my dad did :)
In fact, for kids I'd recommend the walk downhill to the north from Kiyomizu temple in Kyoto – fascinating building itself (on huge wooden stilts), and you walk down through some really beautiful old streets. Some of the shops have goldfish in pools in the guttering! Our two girls loved it when they were seven, three years ago, and it avoids the "not another dusty old temple" complaint.
Certainly do-able in a day from Osaka, and you can get the bus from outside the train station.
Japanes battlefields are variable – Nagashino has an interesting museum, but is too far off the beaten track for you to get to; Sekigahara is dull.
Nara – temples and deer park (tame deer) is definitely child-friendly.
On a more sobering note, I know you said nothing modern, but – Hiroshima?
paints grey horses - specifically, dapple greys.