Part I- The Dreadful Wale and Finding Meagan
Wake up back aboard the Wale. There's a note from Meagan as you leave your cabin. Dr. Hypatia has cleared out, but she's left a touching farewell on the audiograph, and a promise of things to come.
Grab the note from Meagan to Sokolov on the toilet. Other notes can be found under the springrazor off the mainroom, the diary on Sokolov's pillow, and the audiograph by Meagan's bed (she probably noticed your grubby fingerprints on her diary). When you've collected enough, head to the mainroom for your briefing.
You can further explore the ship- a few things have changed. There's a truly mammoth fish in the kitchen, and mannequin on the deck with a bucket for a head. None of these actually furthers the plot, however.
Leave with Sokolov on the skiff when you're ready. Tough on a frail old man like him, but this exposition won't exposit itself.
Disembark, then grab the whalebone off the desk at the top of the stairs, and note the the many flammable bottles nearby. There are also some crossbow bolts and a healing elixir by the big fans here.
Follow the brick corridor to the Bautista Overlook. Some nice looking rooftops, but the Heart tells us all the goodies are up the hill the other way.
Ignore the guards patrolling the Wall of Light, and bear left to the half-buried shop, then make your way up the stairs. There are two guards on the roof- one mostly stationary and one always walking around. Choking out the stationary one can be made even easier by Blinking to the wall behind him, and by the periodic duststorms that hide you from view.
Choke out both and survey the guarded street again. There's only one guard in motion- wait 'til he's heading toward the stairs to the overlook, then drop-stop the red-coated veteran.
Drag him down the alley, then use the awning to go right back roofward. Drop the wanderer, then choke out the blue guard at the balcony- you're too far away from the remaining Wall guard him for him to see (it's probably those ridiculous goggles he's wearing).
Stash the bodies in the shop and then lure the last guard away from the Wall with a crossbow shot or empty bottle (if you choke him out in his current position, Corvo tends to accidentally incinerate him in the Wall. Which is weird on several levels).
He's pickpocketable, so see to that, but once he's disposed off, turn off the windmill and pass through the Wall. Pick up something flammable from the room to your right, then Blink or jump up to the second level to parley with Meagan, who gives you some insight on the road ahead.