This is not exactly the Edinburgh of the early 13th century. I'm adding in quite a lot that was built in the 13th, 14th and 15th centuries because I like them. Also, it'll make the city a bit more interesting to play in. The locations will still be geographically related to each other as they are in real life so a look at Google maps should help you find your way around.
We start at the Royal Castle, sitting atop Castle Rock, The plug of an extinct volcano. A massive fortress with multiple keeps and curtain walls it is, to all intents and purposes, invincible. The long street called the Royal Mile runs along a ridge of basalt from the castle all the way down to the Abbey and palace of the Holy Rood which sits under the hill of Arthur's Seat, another volcanic remnant. On the way down, we pass through the Lawnmarket, where trading in various grains such as wheat, oats and barley happens. This is the only market in the city where the actual goods are not present, the merchants trade amounts which are outside the city itself. We start to find the tenements here, five and six storey buildings that run the length of the Royal mile, packed in on each other.
The tenements are subdivided by their landlords and, with shops on the first floors, the status of the occupants decreases the further from the ground they rise and the further from the "High Street" they are. The tenements spread down the sides of the ridge with narrow lanes called "closes" between them. Many of these are named after the owner of the tenements such as "Milne's Court" or named after what happens there, such as "Fleshmarket Close" which is lined with butchers' shops and has a continual stream of blood running down its gutters. Several of the tenements also have levels underground, with a couple of storeys of cellars. This has led to some of the buildings having levels which are partially inside the ridge and partially exposed on the lower slopes. some closes are, in fact, underground, such as "Mary King's Close".
As we progress down the Mile, we pass St. Giles Cathedral on our right, home of the archbishop of Edinburgh. Just past this is the Mercat Cross, where monthly markets are held, the shops from here extending down to the Tron where the official weights for the market are stored. After this, the High Street runs down the ridge for another 900 feet or so until we reach the Netherbow Gate through the city walls.
Next time we will pass through the gate into the Canongait which runs the rest of the way down to the Abbey.