Salt mines were great - really enjoyed them - we got a Bolt taxi out there and back for around £5 per trip - I think children would enjoy this too - don't panic when you have to walk down about 400 steps to get into them - there is a lift back up! Also the cafe down there is pretty good for trying some Polish food, and is reasonably priced.
There's an illusions museum, and a pinball museum that would be good for kids. Plus they might enjoy castle and fire breathing dragon, a trip on the river, or a walking tour around the main centre or Jewish quarter. Just off the main square there's a trumpeter who plays on the hour from the windows at the top of St Mary's Church tower, and he'll also give you a wave if you wave to him. Near there is the Cloth Hall, which sells (over priced) trinkets and souvenirs, but is nice for a browse. If you don't mind a trip out of Krakow, there's a theme park called Energylandia.
We didn't take kids with us, so mostly hit bars in the evenings, but for eating there's no end of decent places, just don't eat at the over priced restaurants on the main square, it's much cheaper, and often better food, to take a walk away from the very centre. Where you go depends very much on your taste, but there's no shortage of restaurants.
For food on the go, Plac Nowy in the Jewish has a host of stands selling zapiekana - a sort of Polish pizza baguette, which is must try, plus there's a flea market there. There are also a couple of street food truck areas in the city which might appeal to kids (we enjoyed them!). And there are plenty of places selling pierogi, which are worth trying too.