The ghost tours have really gone downhill lately imho. Mercat is probably still the best underground ghost one. Best overground ghost tour is Auld Reekie, which goes to the mausuleum in the locked section of the Greyfriars Kirk, reputedly haunted by the McKenzie Poltergeist (and more recently
desecrated by the daemonically named youth, Sonny Devlin!). Mary King's Close is better from a historical perspective.
People often go up Arthur's Seat for the views, and ignore the much easier climb of Calton Hill, which features the grand Grecian folly which gives the city its "Athens of the North" title, incredible views across the Parliament, Arthur's Seat, Salisbury Crags and Holyrood Palace, and Nelson's Tower which you can go into (except Sundays) and which is crowned by the Time Ball, which was formerly used by seafarers to tell the time. The history of the Time Ball and 1 O' Clock Gun is explained at the Castle, which is definitely worth visiting.
Near to Kings Stables Road there is a graveyard with some fantastic 17th and 18th century slabs.
At the museum, ask a curator where the Fairy Coffins are - I spent a long - but interesting - 45 minutes trying to find them myself before asking! (Clue: They're near the 'funerals and death' section of the new half of the building). Watch out for the witch stones and other rural occult bits and bobs too.
You could do worse than visiting Inchcolm Abbey, a semi-ruined abbey standing on an island in the middle of the Firth of Forth. To get there, take a train journey to Dalmeny station and walk down to South Queensferry (it's not far). Then get the Maid of the Forth ferry out to Inchcolm. It takes a little planning but is well worth it on a nice day!
Have fun.
PS. Gruesome Fun Fact! One of the founders of Mercat Tours was a convicted sex offender and was then
found a couple of years ago, dismembered, in a wheely bin.
