The nearest airport to the Hyatt Regency in Bellevue is Seattle Tacoma International Airport (SEA).
The Hyatt offers shuttle transportation to and from the airport for $19 each way when you book in advance. For more information and to register for this service go here.
If you are interested in other transportation options you can view the airports ground transportation service page.
Bellevue is just east of Seattle. You can get driving directions to the Hyatt Regency here.
Parking information for the hotel can be found here.