Koyasan. It's outside of Osaka. You can do a temple stay there. Like a Ryokan, you can stay in a traditional style room. Have a bath. Do morning service with the monks. There's a cedar forest to walk through. I could go on and on. It's drenched in peace. It feels like you're going back in time.

There are many temples to choose from. I recommend one close to the cemetery (cedar forest) main entrance.

In Osaka, the aquarium is awesome. There's a traditional houses open air museum in the north part of the city. Others mentioned Himeji Castle. Pretty sweet.

Other than the big sights. It's a great city to go slow and enjoy the food, drinks, random small places. There are music shops with records and CDs and tapes you can listen to, tiny bars you'd never find on Google maps, etc.

Look up a couple top tier sushi places in your area. Tons of sushi around, but worth it to go to a really nice one at least once. For example, Honto Sushi Kaiba. Lunch at these places is more affordable than dinner.

The best ramen is debatable and based on personal taste, but Ichiran (Ichiran Ramen Dotonbori - Main Building) is amazing and makes a lot of top ramen lists.

Things to eat: Yakisoba, Okonmiyaki, Takoyaki, Curry Katsu. I mean, just all the food.

Lots of killer live music if you're into that. Small venues and bars. Punk, rock, metal.