Himeji (姫路) is on the shinkansen line to the west of Osaka and has one of the most beautiful castles that is only 15 minutes walk from the JR station. The castle was constructed in 17th century and fully restored in 1960-s. I was lucky to be there in early morning at the best time to see cherry blossoms (and without any crowds - which have arrived later when I was leaving). If you are there and have the time - take a walk around the castle, particularly in the Himeyama Park.
Nara (奈良) was an old capital of Japan in the 8th century and is located in a close vicinity of Osaka. Gardens and temples are only a short walk from the train station and about three-four hours are needed to see the main attractions. Don't forget the frienly deer as well - it is fun to feed them, actually...