From Osaka? You'd be mad not to head to Kyoto and visit as many of the gorgeous temples there of which there are too many to name. I loved walking and walking around this incredible place as many of the best ones (in my view) aren't well known or famous.
Here is a good starting point: http://www.japanvisitor.com/index.php?cID=357&pID=309 about 6 years ago
Kyoto! Sanju-Sangendo, Arashiyama, Kiyomizu-Temple, etc.
If you have enough time, Okayama and Takamatsu/Kagawa are also nice.
It's about an hour from Shin-Osaka to Okayama via Shinkansen (a bullet train), and another one hour to from Okayama to Takamatsu via marine liner that runs on the big bridge across Seto Inland Sea. about 6 years ago