To give you a brief rundown, it is a bustling port city with the masses able to make a comfortable enough living. Technology-wise, it is fairly typical for the Renaissance but its values and ideas come from the late Renaissance, so think the Three Musketeers and similar swashbuckling novels. Romance, honour, glory and vengeance are all very common motivations for the populous. Patronage also defines the city and represents the main method of social movement between the classes, though the upper limits is still very firmly hereditary.
It is ruled by an Oligarchy, a Great Council is overseen by the Potentate and the Council of Ten. The Council of Ten and the Potentate decide the business that is presented to the Great Council, which acts as a legislative body. The Potentate has a veto vote and the Council of Ten is lately seen as his advisors. Both the Potentate and Council of Ten is elected by the Great Council, they are lifetime positions but cannot be passed onto relatives. Being the leadership for the capital, they also have the ability to elect local governors to rule the rest of the country on their behalf. In extreme circumstances, such as war, the Potentate and Council of Ten can disband the Great Council and take the mantle of leadership directly.
Esterwyn relies on the shipping trade from all over the country and even further to fuel it. Banks are common through the city, boosting the trade in the city even further. Esterwyn is famous for its entertainment and merchant districts, while its seafront quarter never sleeps with vessels coming and going at all hours. The government district rings the Watergardens, an area where the nobles establish their villas, both districts combine to form the centre of the city. Major roads are not common in the floating city of Esterwyn, instead canals snake their way through and divide the districts, as such gondolas and other boats are seen through the city. The city does contain a slum area where crime is high but the Potentate and the Council of Ten seem content to contain the issue to the district and ensure that it doesn't spread. Theological concerns aren't really an issue in the city, with most people remaining deeply atheistic but indviduals and the government are generally content to live and let live. At most a devoute and open follower of a god may be scorned, shunned or snubbed but it is unlikely they would become the victim of any targeted violence.
A few quirks of the city is that any firearms are forbidden in the city, after a failed uprising against the Potentate centuries ago. When travellers arrive, they any such weapons to the nearest storehouse that are overseen by the city guard. If this type of equipment is purchased it is sent to a storehouse, to be collected when the individual leaves. In both instances, they are provided with paperwork to prove their ownership that must be presented to the storehouse.
There is also a monthly flat tax for everyone in the city Visitors are required to register in an official tavern or inn when staying and when they do are provided with visitor’s documentation. These papers are used to determine the length of your stay in the city and payment must be made each month or part thereof to the owner of the inn or tavern. One month payment must be made in advance. The city guard can ask for these papers at any time and failure to produce them can see you arrested for tax evasion.
That's all general knowledge stuff that your characters would know entering the city. If you have any other questions, just ask.