The Umeda Sky Building is open from 10:00 am to 10:30 pm(admission until 10:00pm). And the views at night are even better than at daytime. As admission fee is 700 Yen (2001 price) it is advisable to go in the late afternoon and wait until it is dark to see the nightview. You can wait at the 40th floor for the sun to set in the Sky Cafe.
This surprised me. I figured they (amazing race producers) might have played with the opening time, but that is the normal hours.