The tower of Moo Manchu is in The paths of Penance, Mooshu. Just look on your map. You get the quest by completing the side quest 'The Moo Manchurian candidate' which you get from Lord Chagatai in Subata and completing Mooshu. To be honest it is a stupid question considering a lot of other posts have sort of askedthe same question, hope this helped!
The tower of moo is on the Icy dock also called paths of penance . To get this quest you must first have done the earlier moo Manchu quest you get from Lord Chagatai at subuta temple. After completing this quest the town crier ( the pelican in front of Avery's house) will tell you to go see lord Chagatai again and he sends you to the tower Now this I'm not positive about but I think to get the first moo quest you must do the abe pagoda you get that from the chef in the subata tea house. Hope this helps you fair sailing