Check ahead for the National Trust properties as they're not all open. Cragside and Gibside are but I think it's the grounds only and it has to be pre-booked, Seaton Delaval Hall and (I think) Belsay are both still closed.
Northumberland Zoo is a good day out and they have walks through the various enclosures so you can go in with the lemurs and the wallabys, Whitehouse Farm is reopen now too and good for a few hours in the outdoors.
It's easy to spend a whole day in Newcastle City Centre depending on what you want to do. If they're into gaming then The Gate has a gaming cafe (CTRL Pad) and an arcade (YuMe World) as well as some free games in the walkways like giant battleships, table tennis, foosball, etc. Just over the river is the Metrocentre which is a big indoor shopping centre but it also has leisure facilities like a cinema, climbing walls, restaurants, mini golf, and an arcade.
Tynemouth, Cullercoats, and Whitley Bay are within walking distance of one another and you can walk along the seafront to get from one to the next. Tynemouth has a boating lake, an aquarium, surfing, and a long sandy beach. Cullercoats has a small harbour with sandy beach and an ice cream shop/cafe. Whitley Bay had a long sandy beach, Links (promenade) for walking along, arcades, and the Spanish City which has various restaurants and cafes inside. A short walk from there is St Mary's Lighthouse nature reserve where there are often seals on the rocks. All of the beaches have good rock pooling and my DC would spend hours there with a net and a bucket.
Northumberlandia near Cramlington is a huge land sculpture of a woman lying against the hillside with walks around it. Sounds weird but it's a nice trail. Plessey Woods and Bolam Lake are nice for walks too.
I agree with all the places suggested. Beamish is an absolute must-do.