Glasgow Central to Glasgow Queen Street.
Not particularly scenic, I reckon the OP is best looking elsewhere for inspiration
Farringdon UndergrounD to Farringdon Thameslink.
There's no such station as 'Farringdon Thameslink' but 8 steps plus about 5 paces either side of the steps doesn't count as 'a walk' in my book
Helensburgh Upper on the West Highland Line to Helensburgh Central on the North Clyde Line.
Done that. I wouldn't do it in the other direction! Not particularly interesting but I do like to do such walks to see what the places are like. It's a lot easier than Falkirk High to Grahamstone (again I'd not want to do that in the other direction).
My suggestions would be: Whinhill / Port Glasgow to Johnstone / Paisley Canal and Glengarnock to Johnstone / Paisley Canal. We cycled these routes, our route / timings were:
Code:
Whinhill [WNL] 1221 1224 3
Port Glasgow Upper Pass 1259 Pass 1259 On time
Kilmacolm Pass 1322 Pass 1320 -2
Bridge of Weir Pass 1345 Pass 1341 -4
Houston Pass 1400 Pass 1349 -11
Cart Junction Pass 1407 Pass 1358 -9
Johnstone [JHN] 1425 1430 1406 1430 On time
Glengarnock [GLG] 1445 1450 1445 1447 -3
Kilbirnie Pass 1509 Pass 1459 -10
Lochwinnoch 1540 1605 1528 1608 3
Castle Semple Pass 1620 Pass 1618 -2
Kilbarchan Pass 1645 Pass 1635 -10
Johnstone North Pass 1657 Pass No log
Cart Junction Pass 1702 Pass 1649 -13
Elderslie West Jn Pass 1711 Pass 1655 -16
Elderslie Pass 1717 Pass 1657 -20
Elderslie East Jn Pass 1719 Pass 1659 -20
Paisley West Pass 1733 Pass No log
Pasiley Canal [PCN]1744 1711 -33
We linked the 2 routes by getting the train from Johnstone to Glengarnock, to avoid doubling back.
Each route matches the 15 miles in Scotland criteria! Both disused lines, lovely surfaces. Just don't meander around the path without looking though - the surface is so good that some 'racer' types use the path, we were overtaken by some doing around 25mph.
Our timings were based on around 6mph average, with faster timings assumed for the downhill bits. I expect 'rail britain' to keep to our timings on foot though as he
walks at 6mph 
but I'd say realistically each route could be done in 1 day walking. I wouldn't attempt to walk both routes in 1 day.
You could start in Port Glasgow rather than Whinhill. The downside is that there is more of a climb from Port Glasgow (the old Port Glasgow Upper station was a lot higher than the existing station) but the section from Whinhill to Port Glasgow is a bit rubbish, and we were lucky that none of us got a puncture (not a problem walking admittedly).
http://en.wikipedia.org/wiki/Greenock_and_Ayrshire_Railway
http://en.wikipedia.org/wiki/Bridge_of_Weir_Railway
http://en.wikipedia.org/wiki/Lochwinnoch_Loop_Line
http://www.railbrit.co.uk/location.php?loc=Elderslie