What is the typical fee arrangement for construction & bond litigation.

There is not nearly enough information in your question to be able to tell you what your chances of success are. Going after a defunct contractor can prove to be problematic but if that contractor was paid and subsequently did not pay you then you may be able to assert claims against him for violations of the Lien Law Article 3A trust fund provisions. That type of claim could make the principals of the now defunct general contractor personally liable. Claims against the City of New York and against a bonding company (I'm assuming a performance or payment bond) are time sensitive and there are specific forms that you need to file. If you want to explore the validity of your claims further I strongly suggest that you immediately contact a construction litigation attorney as you may be running out of time to assert some of your claims (if you have not already run out of time) to discuss your specific situation. The information provided here is for general informational purposes only it is not legal advice. The only way to obtain legal advice is by speaking to an attorney about the specific facts of your situation.

As to the "going rate" for an experienced construction litigation attorney in teh NYC area - there isn't one. Rates vary based on the type of litigation, the size of the law firm, the experience of the attorney, etc. You can expect to find hourly rates for this type of litigation in the NYC area anywhere from $175.00/hr. - $500.00/hr.