For day trips, Bath, Oxford, Cambridge and Canterbury are all easy to get to from London. A bit further but still doable in a day probably, are places like Warwick (also has a fantastic castle), Stratford-upon-Avon (if you like Shakespeare) or Nottingham which are all very historical places.
Longer away so needs more time are Liverpool, Manchester and Edinburgh which are all great with lots of history.
Flight wise, pretty much any city anywhere in Europe would fit the bill. I'd recommend Belfast, Dublin and Budapest but the real list is so so long!