North Yorkshire coast, maybe Whitby. Is Oxford too far? Liecester can be fun, you have the space centre and soem nice places to eat such as 1573 www.fifteenseventythree.com (unless you are veggi) and the orane tree, not to mention loads of curry places.
Child free for a few days. Needs to be on trainline from NE rail station. Travel time 3 hrs or less. Largeish picturesque town (yorkshire?) or city (not London, Leeds or Edin or York as been there). All suggestions welcome