Does the Mayor have a vote?
In Issaquah, the Executive and Legislative branches of the government are distinctly different. Ava is careful not to blur the distinction between the two branches.
The quick answer is no.
The long answer is that Issaquah has a Strong Mayor form of government like Seattle and Redmond, not a Council Manager form of government like Sammamish and Bellevue.
In a strong mayor system the Mayor is elected by the people and heads the executive branch which is to say the city operations and chairs the city council meetings but does not vote unless it is a tie. In Ava's almost eight years of service as Mayor she only had to break a tie once or twice.
In a Council Manager form of government the Executive branch is headed by a City Manager chosen by the Council. The Council chooses one of their peers to act as Mayor. Because that sort of non-executive Mayor is also a Council member, he or she has the right to vote.