According to a 2001 National Rail timetable, Hinckley is on a cross-country line from Birmingham to Leicester, where it joins the Midland Main Line northward to Nottingham. I haven't checked the National Rail website, but at that time there were diesel mus approximately hourly, 7 days a week--it's the sort of line that in the US would have lost its last passenger train by 1950, but I'd say it's likely that the service is the same today. Transit time is about 35 min. to Birmingham, 20 min. to Leicester, and 55 min. to Nottingham.
There is a light-rail line from Birmingham to Wolverhampton, largely along a former rail r/w with some street running at both ends, and a light-rail system with 3 or 4 branch lines radiating from Nottingham, passing the National Rail station in both cities.
There are two heritage lines within easy reach: The Severn Valley Railway (www.svr.co.uk
) runs from Kidderminster, a short distance west of Birmingham, and leaving from the railway station, to Bridgnorth. It's a classic heritage line, operated strictly according to early-20th-century practice (I can't even guess how many volunteers they have to have to run it, but British heritage railways can apparently find plenty of volunteers.) It's really living history of how railways were operated back in the day. At Bridgnorth there is the Bridgnorth Cliff Railway (www.bridgnorthcliffrailway.co.uk
), a short distance from the Severn Valley Station: a funicular, 200 feet long, 3'-6" gauge, at a gradient of 1 in 1.8 (55%). It's not a heritage railway but has two classic cars and is used by local residents, like the Pittsburgh inclines. The Great Central Railway (www.gcrailway.co.uk
) is an unusual heritage line in that it uses the r/w of the former railway of the same name for about 9 miles and is maintained to permit a track speed closer to that actually achieved by mainline expresses. Since the Great Central was built to compete with the Midland, the stations are not close together, and I'm not sure what local transportation is available. (Any of the above can easily be done in one day.)
If time is short, a good train-watching spot should be Nuneaton, the first stop after Hinckley en route to Leicester, where the line crosses above the 4-track West Coast Main Line, used by expresses from London to Liverpool, Manchester, North Wales, and Scotland--should be a lot going on.
If your friend is a "civilian," there is a National Rail branch line northward from Nottingham called the Robin Hood Line, which apparently passes just west of Sherwood Forest.