The Hyatt is located right near John Wayne airport. It's a very nice hotel. It's only about a 15 minute drive to DL, but with traffic it's more like a 30 minute drive.
I'm not quite sure which great mall fairycat is talking about. There's the Irvine Spectrum which is located in Irvine and South Coast Plaza which is located in Santa Ana. Both are about a few miles from the Hyatt.