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Hi Julie!
If you are searching for some place to visit I recommend you Namba and Umeda, where there are lots of restaurants and shopping spot. Besides, Umeda Tour has a beautiful view of all Osaka^^
There also Tennoji, where you can see temples (there is also a zoo but I didn't go there)... And the Osaka Kaiyukan is quite interesting too (it's an aquarium). Oh! and don't forget Osaka Castle! It's very beautiful^^ but I was a bit disappointed by the museum inside... so I don't recommend you to go inside but if you want I think it's lilke 600 yen.
If you have some time, you can also go to Kyoto, at 30 minutes from Osaka, it is not very expensive to go there, and there are lots of beautiful temples. You can also see geisha if you go to Gion street not to late, around 6PM there are not in the street anymore.

NB: At Namba there is a tourist office, where you can have coupon if you show your passport. And they also give you a good map for all the spot to see in Osaka.

NB2: temples close very early (between 4 or 5 PM) and they are not free (300 to 600 yens). Japanese garden fare are not included.

I agree about the museum in Osaka Castle, but the view from the top is nice and admission isn't expensive. Kyoto has many sights as well. Check out the bamboo forest! And in Nara you can visit the deer park and some historic shrines and temples.