Unless the defendant does business in NY venue is going to be in PA. However, I assume like most states this will be a worker's compensation claim as you generally cannot sue yoor emplyer for on the job accidents.
Carriers are warry of people getting into an accident when their coverage is lapsed and then running to their broker to get their coverage re-instated. The broker is the agent of the carrier so I would try to get a written affidavit from the broker about what he said and when he said it. You may beed to bring a declaratory judgment action against the carrier to determine your rights.
If this is a one-family house in NYC then the City is still responsible, not the homeowner. You need to serve a Notice of Claim on the City within 90 days of the fall. More likely than not the City will ignore you and you will have to sue within 1 year and 90 days of the accident. Unless you have big injuries it won't be worth it. The exception to the above is if the homeowner shoveled the snow and made things worse.
Florida. You have to show the property owner was negligent. Contact a personal injury lawyer in the County where you fell ASAP. Take photos of the defect that casued your fall ASAP before it gets repaired.