My first thoughts on the matter, why Edinburgh, there are lots of nicer places to visit in Scotland, in my opinion Edinburgh is too touristy, its a shame they don't have more time ashore to visit the Highlands, Glasgow, the Clyde Coast, the Southern Uplands etc.
However, given that their visit is going to be restricted to the Edinburgh area, I'd go along with suggestions already made, The Royal Mile, the Royal Yacht Britannia at Leith and of course Scotia Kilts shop opposite Hawes Pier! If time permits, it is only a half hour train ride along the coast to North Berwick where they can view the wild birds on the offshore islands through CCTV, or climb North Berwick Law, or visit Tantallon Castle.