Click on the adjacent city bell to Travel Within Qeynos, and choose The Caves. When you zone in you will immediately be attacked by Guard Belaire who is Level 25 ^^^ Heroic and respawns fairly quickly. This should be the only guard you have to fight.
After killing Belaire, go north east to the right of the first waterfall and swim around the corner to a second waterfall.
Mouse over the base of the waterfall to get the pop-up that lets you travel to The Down Below.
Follow the "water" around to the right to the grate to Qeynos Capitol District - North Qeynos.
You may wish to remove all armor and jewelry to prevent it from being damaged if you get caught by the Qeynos Guard. If you are anywhere near the appropriate level for this quest it won't help you anyway.
In Qeynos, head along the wall to your left until you reach the first building, which is the Qeynos Guard Barracks. Go down in the ditch and right along the barracks to the door. Watch out for the mounted guard that infrequently patrols up to that door from around the far corner of the building.
From the door head toward the large tree, and straight on to between the two park benches and on to the back of the Ironforge Exchange.
You need to watch out for patrols on the main north-south road that goes under the aqueduct, and foot patrols along the wall to your left at the edge of the canal.
Move to the aqueduct keeping halfway between the main north-south path and the canal path, and take a last look around for guards.
When the coast is clear run north-east across the north-south road to Clothspinners. If you make it inside without being seen you're safe.
Peona Toughins will refuse your business, but you can hail her using the right mouse button and 'hail' to finish the quest.