If you like motorsport there is the Jim Clark museum in Dunns just over the border in Scotland. I’ve not been for years but I remember it being small but interesting. It would be a short stop on a trip up to Eyemouth.
If the tide times work then spending time on Holy Island when the tide comes in is lovely most of the day trippers leave and you have the place to yourselves.
The other recommendations all seem really good and it has reminded me why I need to plan another trip back to Northumberland.