I worked up there last year - its 5 hrs door-to-door (max) and a piss-easy drive.
Better airport is teesside but few airlines travel there.
Newcastle is a 'mare of an airport and you'll spend a small fortune in taxis, buses/trains.
Looked into Tee-side but couldn't see much, especially from Brum and Bristol Airport. Am selling my car so would have driven otherwise.