If you have a free day, Koya san would be a nice place to go. The Osakajo is nice to walk up to. The structure itself is concrete with an elevator inside.

For food, the teppanyaki place in Hotel Granvia over the JR Osaka station is very nice but closer to 15K yen. There are many eating places in the walking streets just to north and east of the Nankai Namba station, of every type and price points. Don't miss the smaller places in the back alleys. Places on the front streets tend to be mass market oriented but back alley tend to be nice traditional places. Sept is a little to eat fugu but this is a place on the main street in Nipponbashi just to the east of Namba. You can't miss it, it has a huge fugu out front.

For traditional night spots, Kitashinji just to the south of the JR Osaka station would be the place. There are many bars and what not north of Namba. For more raunchy places, they are around the Hankyu Juso station and at Sakuragawa to the west of Namba.

Kobe is a narrow strip between the bay and Roko mountain. Busy place would be Nishinomiya. There is a large shopping complex on the way to Kobe off the JR Amagasaki station. There are many restaurants on both sides of this station.