If you decide to fly to Osaka, the Sheraton has a great transportation option, which we did last year. From their website:
Limousine Bus

Fee:
Fees are per person, per way. Adult - 1550 JPY, Children (under 12 years) 780 JPY
Hours:
Bus departs from the airport to the hotel every 20-30 minutes.
Hours of operation
Sunday
6:00 AM - 10:35 PM
Monday
6:00 AM - 10:35 PM
Tuesday
6:00 AM - 10:35 PM
Wednesday
6:00 AM - 10:35 PM
Thursday
6:00 AM - 10:35 PM
Friday
6:00 AM - 10:35 PM
Saturday
6:00 AM - 10:35 PM
Travel Time:
55 minutes
About:

Limousine bus is available on the first floor outside of KIX terminal building. Before embarking on the bus, please purchase a bus ticket at the vending machine located near the bus stop. The bus destinated to "Kintetsu Uehommachi" leaves from bus stop number 7 and stops in front of our hotel.