TU154,
Newcastle International (EGNT) itself hosts a busy helicopter flying school -
http://www.northumbria-helicopters.co.uk/ who may be able to advise you on fees at the airport. From here you can get a train (the Tyneside Metro), bus or taxi into the city centre - 20 mins.
Also you might want to consider Elwood which is about 15nm to the west of EGNT
http://www.northumbria.com - its a bit difficult to get into Newcastle - you'd probably have to get a lift a few miles south to Hexham and then get the train.