Ok.
Ouseburn area, to the East of Quayside (drive or take the bright green Quaylink bus) has become very child-orientated. The Round www.the-round.com is a theatre aimed at children and teenagers. I haven't been, but some of the plays I've seen advertised sound great.
Next door, Seven Stories www.sevenstories.org.uk is great! It's the first centre for children's books in the UK, is set over 7 floors and has loads to entertain kids and parents. At the moment there is an exhibition of naughty characters (dennis the menace, horrid henry, peter rabbit, pippi longstocking etc.) that's really imaginative. Older kids and parents will like looking at writers' manuscripts, artists' original drawings etc.
There's also an ok cafe here with healthy kids food, although I'd go 2 doors down to The Cluny, a great pub - the kind you'd actually want to go to without kids - which is child-friendly. Quite bohemian, very relaxed, decent food and great beer.
You could easily spend a day just in Ouseburn area.
The Sage occasionally puts on family concerts, so have a look at listings. It's a very interesting building, but if there isn't a concert on ,you probably won't stay long. Planet Music is a 'music making' group for 5-7 year olds on a sat. During the week there is "music Making' for under 5s - my DD loves this. Different people go each week, so if you're a visitor you won't feel like you're infiltrating a tight-knit group.
Baltic has a floor dedicated to 'learning', which means books, films etc for adults and play stuff for younger kids. On saturdays they have children's sessions to make art.
In town, the Laing gallery also puts on saturday craft activities, plus has an under 5s play area - great for a break from the shops. The Discovery Museum has loads of fun stuff for kids,as does nearby Centre for life (hands on science museum). Discovery is free though!
What kind of a place to eat are you looking for?