I'm trying to understand the following sentence:
The (New York) city council is congress to the mayor's president.
What does this sentence mean?
What (who) does the mayor's president refer to?
The City Council has the same kind of relationship to the Mayor as the US Congress has to the President.
This is a specific structure to compare two things.
A is to B as C is to D.
An example is:
Green is to go as red is to stop.
In the context of traffic lights, green means go and red means stop.
The City Council is to Congress as the Mayor is to the President.
So in the context of politics, the local government City Council has the same relationship to the federal government Congress as the local government's Mayor has to the federal government's President. In both cases, an aspect of local government is being compared to the equivalent aspect of federal government.
Your example sentence is confusingly worded, but that is what it's trying to say.