I can think of loads of fascinating places ...
Pump museums - Abbey Pump Museum, Leicester (next door to the space centre, which is fascinating as well), Papplewick - don't forget the tour of the reservoir at the top of the hill, and have a look at the coalmine winding engine house (it works!). Visit both of these on open steam days.
The whole of the Ironbridge Gorge - get one of thier annual passes, you wont' regret it! And walk the fileds around the gorge, peering into the undergrowth and at likley lumps and bumps. Walk the streets around and above the town, and look at the buildings, not just the museums. Jackfield church is a delight, once you spot the bricks and tiles advertising the local companies wares.
In the peak district - walk around the fields above Brassington and up to Harbourough Rocks -lots of evidence of "cottage Industry" lead mining, all over the place - you can tracethe direction of the lead seams from the bumps in the ground! Have a walk up from Wettonmill to Ecton, where you'll find the remais of what was once the deepest copper mine in the world.
RAF Cosford - mind-blowing in parts, scary in others (what the Germans achieved in WW2, what the kamikaze pilots flew, and the cold war stuff), interesting everywhere.
Old Warden aerodrome - I spent hours there. It also has gardens that the little lady can visit when she gets bored!
Beltchley Park, and the computer museum (which I think is now separate)
Birmingham Museum Collection centre, they have an open day once in a while.
The Finch foundry at Sticklepath, near Okehampton.
The Cornish coastline - and some inland places as well (tin and copper mines, and clay pits)
The Peak District Mining Museum in Cromford - and the canal that runs from there to the junction with the High Peak Trail, visit when the pump is in steam. And walk around Cromford itself.
Quarry Bank mill.
I could go on ... - oh, I have!
Can't wait to visit places such as Sutton Hoo and Grimes Graves
Brompton, Condor Heritage, creaky joints and grey hair
""You know you're getting old when it's easier to ride a bike than to get on and off it" - quote from observant jogger !