This is going to be very short and very sweet.
Manor Mysteries 1 is available I believe when the mission " The Wedding " is completed. At least it was for me!
1. ) After activating the mission, head to New York via Harbor Fast Travel or whatever means you see fit.
2. ) You can use a fast travel once you arrive, either way - head to the burned section of New York which is North and a bit West of your location.
3. ) Follow the Green Mission point and climb the burnt building. It's also directly under a fast travel station as well. -- Make sure you watch where you drop down or else you'll fall to the bottom and have to climb again. --
4. ) Use the " Interact " button for whatever system you have and claim your prize.
5. ) Fast travel to the nearest harbor, to fast travel to Homestead.
6. ) Go back to see Achilles.