It's got to be the airport bus (Osaka Airport Limousine) at 1,550 Yen one-way per adult, and 780 Yen one-way per child. It leaves directly from the airport terminal. From memory, I believe it arrives right in the middle of Osaka at the Hotel New Hankyu. Just follow the signs through Umeda Station (where the Hotel new Hankyu is) towards the JR station and look for the Sakurabashi exit. Keep walking straight ahead, cross the road (under the bridge) and walk through the small Plaza full of mini restaurants and an electronics shops. Follow the road straight up and the Monterrey is on your left. That's about a 10-15 minute walk with children...perhaps a bit longer in the rush hour and with the two sizeable pedestrian crossings. If you have baggage as well, it might be an idea to jump in a taxi at the Hotel New Hankyu - there should be loads of them parked up there. It's a short hop (1,000 Yen I would guess) but it will still take the driver about 10-15 minutes to get there with all the traffic. Hope that helps.