I was only ever a crew in that area so I have no idea about costs:-
The marinas in that area are Roker (Sunderland); St Peter's (under the High Level in Newcastle) - LONG way to the open sea; Braid (Amble) municipally owned but operated by C&N - LONG and possibly expensive hike up the A1 as every speedcam is loaded with film.
I don't know about Blyth, but it is well located.
If you have a bilge keeler prepare to get very muddy.
Enjoy your sailing there and send my love to Lindisfarne (Amble YC and Royal Northumberland YC (Blyth) have deep water moorings there).
There is also Royal Quays at North Shields but its rather expensive.
I think Amble is not now operated by C&N but is privately owned. I don't know the present cost but it was quite pricey 3 years ago.
Blyth has pontoon berths but they are run by and for the RNYC. They have visitors berths (who are treated most hospitably) but I doubt they have berths to hire.
St Peters is quite good fun - I got inspected by the Port Health Authority there once (the boat that is not me personally). Its about 9 miles to the sea.
Sunderland has a marina but they seem reluctant to let berths for some reason. At least when I contacyed them everyone referred me to someone else.
Hartlepool is the cheapest at about £110 per meter and it has probably the best facilities too.
There are a number of trots of moorings all along the Tyne but I have no information on any of them. Friars Goose opposite St Peters may be a good place to start asking.