There is a map floating around that is correct on all locations EXCEPT the city island. City Island is reached by going 60-65 paces up then just keep going east until you see it.After completing 100% of the Book visit the city and reload to the main island. Now you can obtain the recipe for Mysterious Engine. Once you get that recipe you can enter the City and access the Antique Shop. You can only enter the City during the daytime.