Things to see in Osaka:
Universal Studios Japan - self explanatory (I haven't been there yet, I had dates to go there on two different occaisions but it rained both times🙁 )
Nipponbashi - a lot like Akihabara, lots of electronics, anime, adult goods, and other stuff you don't find anywhere else
Osaka Castle - it was rebuilt with concrete so it's a lot more accesible than other castles like Himeji, has some nice exhibits about the history of Osaka and Toyotomi Hideyoshi inside
Umeda/Kita district - near Osaka station, basically downtown Osaka, with all the major department stores and one of the world's largest underground shopping malls
America Mura - also known as Amemura, has lots of clothing stores that teenagers frequent, also a bunch of clubs and music stores. More centered toward hiphop and rap
Dotonbori - located in near Namba area, lots of good restraunts and nightlife (similar to Kabuki chou in Tokyo), also walk towards Nambe for shopping and things
Osaka Aquarium - has a whale shark and a huge tank in the middle
I don't know when you are going but there are a lot of good festivals in July and Aug. Plus Kobe, Kyoto, and Nara are each only about an hour away by train.