Only just found this on the GN email, and the OP still hasn't responded - weird?!
As was mentioned, it's a guess where they're starting, also budget, and how much time to fill, but assuming Cambridge area, well, London has more to do than most (but it's often packed with tourists!). Edinburgh had a mention, and that's a good choice, Glasgow too (more to do than many realise).
And for a short break, Ludlow & Shrewsbury are good, as per a couple of comments, but my personal favourite is York, just gorgeous).
IF they can go abroad, then the Eurostar (St Pancras) is a good start, with Paris, Lille, Lyon, even Bordeaux all within reach (but beware the summer heat in Paris?).
Italy is reachable by train, the excellent Seat61 website has masses of info about loads of places, one idea is to route through Switzerland for that lovely scenery en route to perhaps Milan? Milan and/or Turin are both great, and from Milan a day trip to (Lake) Como is simple.
If they have a week (& the money!), a Rhine cruise ticks a lot of boxes!