Vendor vs. Service provider to a government enity.

First, your situation will be covered by the law of the state where you are located, so without knowing where you are located, an attorney wouldn't be able to give you much of an answer and then you will get an authoritative answer only from an attorney licensed to practice in your state. That said, let me comment on a parallel situation in the federal government. It is not clear exactly what service the city is receiving, but if there is an identifiable benefit to the city, in the federal context we would use something called a cooperative agreement. It's a contract in the broadest meaning, but not a procurement contract and it is authorized by federal law. When they say you are not a “vendor” that is what they are referring to. They aren't paying you money so you don't have a procurement contract and therefore aren't a vendor. But your state law might provide for other types of agreements with public entities like the cooperative agreements at the federal level. That type of agreement would identify the benefit flowing to the city and what they are going to do for you in return. You might run into competition requirements for any kind of agreement so you might offer this as a test arrangement to see if it makes sense for the city.