There are two interesting stanes in St Andrews, and the other day I went and photographed both of them for you.
The Black Stone is on display in a glass case in the Museum of the University of St Andrews, though I remember years ago before the museum was opened, seeing the Black Stone standing in the big fireplace in Parliament Hall, below the old library. Apparently it used to be used as the ritual seat on which MA candidates would be seated, for their oral examination, and it was used for this purpose from c.1420 (when the University was brand new) through to the 18th century. It looks like it may be a Roman pillar capital; the bands are gilded, and it is extremely black. It is obviously connected to other ritual stone seats such as the Stone of Scone at Edinburgh Castle, and the Frith Stool in Hexham Cathedral.
The Blue Stane stands behind high railings, outside a pub of the same name, on one of the roundabouts on City Road, a hundred yards or so outside one of the old medieval gates of the city. It has moved around a bit over the centuries (since its first appearance on a 1580 map) but has always been beside a road outside the West end of the city. It is a kind of Dolerite from Drumcarrow Craig a few miles west. In olden times, men would pat it and women curtsey to it as they passed. It is said to have been King Kenneth MacAlpine’s coronation seat in the 9th century. Apparently there is another blue stane outside of Crail kirk but I have not seen that one.