Whitehouse Farm and Northumberland Zoo are both open now, you have to prebook via the websites.
All of the local authority owned play park are (or should be) open so that includes the ones at country parks, I'm almost certain Druridge Bay park is open as friends are going this weekend.
Plessey Woods is good for walks and has a nice play park that was recently updated. There is a huge sculpture near Cramlington called Northumberlandia which looks like a woman carved into the hillside and there are walking trails around it. Down at South Beach in Blyth is a play park with beach huts, a land train, and a WW2 battery.
Seahouses has everything you'd expect from a tourist seaside town and has arcades. You can get a boat from there that will take you around the islands to see puffins and seals.
If you come down the coast a little there is a nature reserve at St Mary's Lighthouse, rockpooling, and there are often seals on the rocks. The local sealife sanctuary releases rescued seals sometimes too which is nice to watch. Just along from St Mary's Lighthouse is Whitley Bay which has arcades, a nice park behind the arcades, and a nice beach. That whole stretch right along to Tynemouth has various little play parks, rockpools, and beaches. At Tynemouth there is the boating lake, inflatable slides, a pirate themed maze, dinosaur mini-golf, and a play park. They're all outdoor so are open now, across the road is an aquarium too.
If you don't mind going south of the river there is an amusement park in South Shields with a funfair and arcades on the beach front then across the road is a big park with play areas, mini railway, duck ponds, and boats.