Osakajo and the park that surrounds it. It is a reconstruction, yes, but still impressive. The destruction of the castle, the siege and battle, were major events in Japanese history. There is a work of art (woodblock print, I think) that gives a sense of the day that the castle was overrun. Not pretty. Understanding the history that led to that, what happened there, and the events that followed made visiting the site meaningful to me.
More later

My only experience with Kobe is the ropeway. It is right at Shin-Kobe station. I took the ropeway up, nice views, walk down, and then back on the shinkansen,

Osaka is famous for food. The saying is that Kyoto-jin spend all their money on fashion and Osaka people spend it on food. Okonomiyaki and takoyaki, also found a nice kaiten sushi place at the station, and Kobe beef, There is a national bunraku theater, short program with English headsets, but I was too jetlagged to enjoy it. My second visit to Osaka was for cherry blossoms at Osakajo Koen and another location. I used Osakajokoen station to access the park, but that is sort of the rear entrance, so I recommend the main entrance (Otemon Gate) to the southwest so that you see the front of the castle as you approach. Go on through to Osakajokoen station on the JR loop line. Actually, arriving at Osakajokoen station worked for me because it was pouring rain and there was an event hall / arena nearby. I didn't was going on inside but I bought a ticket to get out of the rain. It was a cheerleading competition which was fun to watch.

Also, Spa World is great.

On second thought, I think it was a marching band competition, not chearleaders.
(i think this post might appear before my last post which is in limbo)

thank you!

Saying in Kobe puts you closer to Himeji Castle, which I prefer over Osaka Castle. Himeji is original while Osaka is rebuilt.

Osaka Aquarium
 

Has anyone been to the aquarium? I love aquariums (my favorites so far are Lisbon and Monte Carlo), and wondered whether the one in Osaka is worth visiting.

Osakajo is not even that. It's a modern museum with a castle facade. Himeji though is the real thing. The Kokoen Garden nearby is also beautiful. Hikone also has a charming castle (and one of the originals) that is gorgeous during cherry blossom season.
The Osaka Aquarium Kaiyukan is one of the best in the country.