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Osaka Castle.
I forgot to mention if you want to visit some of the castles in Kyoto/Osaka you'll have to find a place to park your bike. Some don't want bikes inside. Never got to go to the Nijo castle because there was nowhere to park your bike and it was raining. If you want to do sightseeing it might be best to just park your bike outside the hostel/hotel for the day and use public transportation. I would not recommend riding around the cities with your bike touring gear. It is a nightmare. You become a huge inconvenience to people and it makes basic tasks complicated.
