Some really good suggestions here.
Alnwick for a day is easy, barter books to get second hand books, lunch in the cafe, then Alnwick gardens, and lilidorei.
Amble harbour, puffin cruise and then either lunch at the chippy, or if you go later the week there is a brewery (Brewis Beer) that have food stall Thursday, Friday, Saturday and Sunday and always have some really nice food offerings on.
As others have said lots of lovely countryside walks or towns you can visit. You can do a nice walk down by cresswell and go to the Drift Cafe which is nice and friendly and decent food options.
We love Whitehouse Farm as it’s super fun for children and they have lots of activities and things to do but don’t expect much from the food, pretty standard fare.
Places to eat that are lovely - jolly fisherman in Craster, the boathouse or the fish shack in Amble, Lobo rojo in Whitley bay. For nice family meal Lolly Rosso in Morpeth has always been good for us.
If you have a car I can also really recommend driving into Newcastle and heading to Ouseburn - there is a children museum based on reading (seven stories) and then next door Ouseburn farm, so you can get indoor or outdoor (or both) and then get some food nearby at patty melts for example.