We took the kids on the train to Durham and came back the same day - 2 hours down, 2 hours back. We did conclude that 3 hours, not 4, are required to do Durham with kids.
We visited the cathedral, which is FREE and amazing! You do have to pay for the special collection but it is well worth it.
Sadly you're not allowed to take photos inside the cathedral.
They have explorer-style backpacks with binoculars! Info booklets, stuffed toys and other fun bits are included. Upstairs we dressed up as monks - 'too itchy,' my children announced. I tried to explain it wasn't itchy enough for some monks who also wore hair shirts. My children were not amused.
We took a stroll around the river.
There were sticks. Also a Krispy Kreme's. What more could you ask for?