My Way or the Skyway

Nearest porticulum: Miran Gate. The "skyways" are small bridges between the buildings in the Public Market area. You climb over the roofs to walk on their roofs. The map uploaded here by spooky01 is perfect. The City Core Puzzle is on the triangle part of this roof, so if you can get to that you're in the right place - don't jump down to it for Skyways 1 and 2 though. Skyway 1: Start at the worldstrangler root at 6980, 10045, and climb it to the roof of the largest building, run all the way across the roof to the Northwest tower, out across the roof of the arch, and you can then un-mount, jump down to the roof of the bridge. (I ran up and down it to get the achievement credit, but I think you just have to get past the middle) Skyway 2 is underneath of and at an angle to Skyway 1 - you have to be on Skyway 1 to get to it. From a little way along SW1, fall down to Skyway 2 (if you are too close to the tower/wall, you'' overshoot and have to climb up again, especially if your alt has speed boosts active.) Note: There are 3 artifact spawn points on Skyway 2, one at each and and one in the middle. Skyway 3 - Now follow the same path up the worldstrangler root to the roof, and this time jump down to the triangle roof at the North end. (You'll find the puzzle here - if it says you need knowledge of a Knight's Tour, you can't do it yet.) At the top right of the triangle, the jump down to a square roof is easy and from there line up the coloured tiles to get onto Skyway 3.

Correction to Maulbeere's otherwise excellent description: Skyway 1 is reached from the northeast tower of the quadrangle/roof, not the northwest.