As luck would have it, the first Big Town selected at random is within easy striking distance of Sheffield. I can get there in an hour and twenty minutes for £12.50 return - it'll probably be the cheapest trip of the tour. It has a unique and famous industrial history, and it's on a waterway - one I've not boated on and possibly never will.
By amazing coincidence, I visited there last year - and for the explicit purpose of visiting too, not to do or buy anything, or to see anyone, but just to visit the place. It was well worth it too. I've checked, and I didn't blog about it at the time, so I could just cheat and post some of the photos from that visit (and I probably will, but honestly, because I have some nice ones, and it was sunny) but one thing I didn't see was the station. This one did fall victim to Beeching - but was resurrected nineteen years later. So next time I have a free weekend I'll go again. I wonder if these two things I didn't buy but wished I had will still be there.