From Long Beach Airport: Take a cab! The Hyatt Regency has a negotiated flat rate of $23 from the airport to the Hyatt Regency Long Beach. Less expensive than SuperShuttle and no stops along the way.
From LAX: Super Shuttle has a rate of $17 to the Hyatt Regency Long Beach. Please mention the Hyatt Regency Hotel in particular, not simply "Long Beach". A cab will cost $65-$70.