Populate series of drop downs from Api web service

We have a CX survey where the user needs to select the location where they had work done. With over 3000 locations possible for them to select, we are looking for the best solution for this selection. This is important since the CX results are assigned to that location they select. We are over the limit for the drill down question.

Another thought is to ask a series of location questions using an api to filter down the data to the specific location. First State which would populates a drop down with filtered cities for that state. Second City which would populate the listings of dealer locations that are within that city. They would choose from this dropdown for the CX survey. In theory, it sounds like it would work, but I am running into major roadblocks.

Any ideas?