Morning: start your trip with the cool life-size diorama reproductions of Edo life at the Osaka Municipal Housing Museum "Osaka Museum of Housing and Living"!
Then head down to Dotombori District for lunch! In my opinion this is the highlight of any trip to Osaka. You'll find a level of joyful chaos and creativity here that's unmatched in any other Japanese city.
When you get tired of eating, head down to the amazing terraced garden at Namba Parks. For some additional souvenir shopping, head down to Osaka Takashimaya for a taste of old-school Japanese department store culture.
Head back to Dotombori District for dinner.
Chibo Okonomiyaki Restaurant is particularly famous for okonomiyaki, which is a type of Japanese pancake!
Wander through the lantern-lit alleyway of Hozenji Yokocho to find a bar for dinner.
Day 2
Morning: head down to Osaka Castle on the early side - it opens at 9:00 AM.
Afterwards, walk around the Nishinomaru Garden!
Then head to the Osaka Museum of History for a little more local color and some more cool dioramas. Or if you've had enough history, head out to Nakanoshima Museum of Art, Osaka (NAKKA) instead for some great surrealist art.
At sunset, head to the Kuchu Teien Observatory at Umeda Sky Building for skyline views of the city. Then grab dinner in one of the countless shopping malls in Umeda.
Day 3
If you have a third day in Osaka, I recommend going elsewhere in the Kansai region - either to Himeji Castle or Nara Park, both only a few hours away by train.