Pedro here's the link to St Giles Cathedral, worth a visit and right on the Royal Mile. It's free entry, you can make a small donation but don't bother there's plenty of money in Edinburgh as it is.
http://www.stgilescathedral.org.uk/history/
Just past St Giles you might see one of Edinburghs customs, people spitting on the 'Heart of Midlotian'
The Heart of Midlothian on the Lawnmarket besides St Giles Kirk in Edinburgh, marks the site of the former entrance to the hated Tolbooth Jail.
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This prison had occupied a very small space but stood five storeys high and with dungeons two storeys beneath. The conditions inside were notoriously poor. Some people died in the Tolbooth prison, not through being executed but simply from the conditions and they treatment they received at the hands of the Edinburgh Town Guard. The result was that both the Tollbooth Jail and the Town Guard were utterly despised by the citizens of Edinburgh.
Were that not enough, as it's name suggests, the Tollbooth was also an excise house where local taxes were collected. Many of the tax levies in old Edinburgh were extortionate, so the Tolbooth became hated for this reason as well.
The spot of execution is today marked out in brass setts in the ground on the corner of Lawnmarket and George IV Bridge.
Another tradition is the story of Greyfriars Bobby
http://www.royal-mile.com/famous-scots/greyfriars-bobby.html
It's probable that the story was a rather clever publicity stunt dreamt up by Victorian traders to boost the economy around the site and it continues to do that over 150 years later. One of the main beneficiaries of this continued interest is the local
http://www.nicholsonspubs.co.uk/greyfriarsbobbysbarcandlemakerrowedinburgh/