The Captain's Quarters are atop the Hub to the right of Main Street. You will need the code (0516) from Mayor Crumb's office, and use Sprocket and the robot crab to restore the power to the Hub's elevator. You also need the old vine from the roof of the Storeroom left of the Living Quarters.
Get the robot crab and Sully's key at the Living Quarters building, and the Old Vine from the roof farther left. At Sully's, reactivate the robot Sprocket and then have him drop the crab on the Hot Hatch below the Hub. Underground, use the old vine to defeat the monster and solve the puzzles to restore power to the elevator. Climb the hub and take the elevator to Ziggs' quarters.
the crab on steamworks island is next to the living quarters
get the crab from the living quarters
0516
It is at the far left past the living quarters. It is covered by vines that have to be removed.
There are no windows that open inward on Steamworks Island. There is a skylight in the City Hall that can be opened with the Multi-Tool. You go out the hatch above Zack's room in the living quarters, to reach the Mech Crank on the vines.
The "rope" is a coil of old vine on the roof of the , left of the Living Quarters. You need it underground at the Hub.
its in the museum on mainstreet of steamworks island :)
It's Steamworks Island #14th Island
(The solution is at the related question "How do you beat Steamworks Island")
The captains quarters is in rockhoppers ship Hope this helps Stepheny1(clubpenguin account)
When Sprocket is grabbed by the vines at the Captain's Quarters, slam the metal windows shut to cut the vines.
SPOILER WARNING: The citizens of Steamworks Island had to hide from the plant monsters that they created so they hid themselves in a hibernation area for 200 years. The path to their chamber is through the plant-covered annex at the far left of the Living Quarters area.