North Yorks Moors Railway

A preserved steam railway.
The line runs 18 miles from Pickering to Grosmont, with a total of five stations. There is a connecting service onwards to Whitby on the coast, also apparently steam hauled. Network Rail trains serve Whitby and Grosmont too, but the tickets may not be valid on both services. For the enthusiast, the stock book lists about a dozen each of steam and diesel locos, and several dozen coaches and wagons.
The website says that on some dates services are available along the Esk Valley line, which runs from Whitby via Grosmont to Battersby – a 24 mile run, but I couldn’t find any timetable, so if you are interested you should telephone them.
FYI, the Esk Valley line is normally used for the Network Rail Whitby-Middleborough service.
Of the stations, Pickering is a tourist destination, with a castle, Goathland is the film set for “Aidensfield” in a well-known TV series, and Whitby is a port and seaside resort, and folk festival venue. The NYMR base is at Grosmont.
I remember breaking my journey at Goathland for a lengthy walk which stretched my enthusiasm for walking far beyond its limits as I tried to reach some now-forgotten goal. There is a pretty gorge with waterfall near Goathland which is a popular destination for walkers if I remember correctly.
As for the train trip, I was somewhat disappointed to discover that the line lies mostly in wooded valleys with no view of the moors. You can see more of the scenery by driving the A169 from Pickering to Whitby (or at least your passengers will :-).)
This railway is worth a visit whether your interest is fired by tourism or a passion for steam trains.