We had a quick walk around part of the castle's moat before crossing a bridge that took us to the castle grounds. We were there around 9am and the weather was not great, but there were still a ton of people; I would definitely recommend visiting at the beginning or the end of the day (last entrance is at 4:30pm). We stopped to take some pictures of the exterior (I was particularly excited to see a 'Japanese Castle Emoji' in real life!) and the yellow statues for the Tenka-Ichi Festival, and then joined the queue for tickets to enter the museum.
The castle itself is a 1931 concrete reconstruction of the original 1583 structure, and most recently underwent some restoration in 1997. Visiting the grounds is free, and 600¥ will get you into the museum, which covers the history of Osaka and the castle over eight floors, and has an observation deck with 360 degree views of the city at the top. The displays flow from top to bottom, so you can take an elevator between floors, use the stairs, or any combination thereof; the most popular mode seemed to be taking an elevator to the eighth floor and then walking back down.
Displays included original artefacts and documents, as well as replicas and models of to show what Osaka looked like over the centuries. The museum had to work within the confines of the castle building, which is deceivingly small, so sometimes the crowd doesn't flow very easily, but there were enough displays and mounted information that there was always something to look at or read. One of the floors had a photo shoot area with costumes, so Clem enjoyed dressing up as a soldier (at the cost of ¥300).
We were back out of the museum within about an hour, and then we walked over to a garden of blossoming plum trees we'd seen from the observation deck. It was still a little early for the trees to be fully in bloom, but I still took advantage of all the gorgeous hues of pink and snapped away. From there we walked the rest of the moat's perimeter, and headed back to the train station.
Osaka is known as "Japan's Kitchen," so I would have liked to spend a few days there just eating, but unfortunately the timing didn't work out with the Kyoto trip. Hopefully I can return sooner rather than later!