Here's an alternate idea. From KIX, take the high-speed ferry to Kobe. Walk around Kobe area for shopping, something to eat, etc. Lots of things to see in a less hectic and more compact space than Osaka. Maybe take ropeway to top of Mt. Rokko. Return by ferry to KIX at end of day.

If you want historical sites and old Japan, then Kyoto is best, or maybe Himeji Castle. If you want the hectic downtown Japan feel, then Nanba works. If you want a bit less hectic, but want to walk around and window shop, then Kobe might be good.