Sort of this, although I find if you steer clear of the area immediately between the station and the river/just the other side you should be ok. It’s what I’ve tended to find anyway! No doubt it’s better and quieter all-round during the week though.
Scarborough is nicer than it’s given credit for, and has plenty to do. You can combine it with Whitby/walk between the two if you have the energy. If you’re used to coastal stuff it might not have quite the same novelty though.
Leeds has got some free museums and plenty to do, but might not be as fun for children your age. I’d buy you a pint if you came to Leeds (although again, might be a hard one to sell to the kids haha)