Where the sidewalks are safe in most worlds of the Spiral, Marleybone takes place on the rooftops of the buildings in that world. The safest place on a rooftop is far from the edges, so stick to the middle and watch for creatures darting across!
Walking down the middle of the rooftop has always worked for me-but when around running monsters such as Gearheads, I find that it is easier to run behind one of them at a safe distance. That way, you can't be caught by surprise.
You can't get through the rooftops in a hurry. Each group of enemies has a certain pattern that they run. Take 20 seconds to watch that pattern. With the cats and rats, the middle may be best, but with the golems - watch out! they run as fast as us and criss-cross the middle or turn in a circle. If you have watched their pattern, you have a much better chance of getting through, but no method is foolproof. Good Luck!
I find one of the most annoying things to be is when you are exiting combat you get sucked right back in by something that either spawns ontop of you or walks right up behind you as you are leaving. Seems to happen more in Marleybone then anywhere else.
Really wish there was like a 5 second grace period after leaving combat before you can be pulled back in.