Discovery & Hancock are free
Customs House at shields is really cheap for cinema (£16 for family of 4 not sure on individual prices)
Metro day saver is good to do a round trip and include the shields ferry getting back on the metro at the other side this only costs about £3 all in and is a really fun day out (especially if you include fish and chips at the fish quay before getting on the ferry!)
Metro to the beach with a picnic.
Saltwell Park is fab and free
Swimming is quite reasonable at the council run pools West Denton etc.
There is a free train museum at Shildon if you drive?
jam jar with a string handle is great for 'fishing' in rivers and investigating your catch....
Nature trails in woodland parks...loads of them in the area (Newburn, Rowlands Gill etc)
Chalk pictures on the patio? (easily cleaned up afterwards!)
Baltic is free and they generally have craft events over the holidays
Walk along the quayside over the millenium bridge
is lovely on a nice day
Shall try to think of more...