Advice on car parks and hotels near Newcastle airport

The Premier Inn and Doubletree are both a very short walk to the terminal. Premier inn does not have long term parking but we drop our bags at the hotel then leave our car in one of the airport car parks. We prefer the meet and greet which is very efficient. We recently used code PARKUP22 for 10% discount but it may have expired. The Britannia is also on site but gets very poor reviews. Other hotels sold as airport hotels including another premier inn are a few miles away.

Can’t help you with recommendations and you've probably seen that 3 hotels - Double Tree by Hilton, Premier Inn and The Britannia are within ‘spitting distance’ of the airport? Those are in National chains, so I expect much the same standard irrespective of location.
Car parking at the airport itself, in the long stay car park cost us £60 for 5 nights, but I suppose staying longer might get a better rate. It’s only a 5 minute walk from the terminal. Don’t get into the short stay or drop off car parks as you’ll need a bank loan to get out - or just hand over your car!