Head terms in the five boroughs already belong to the aggregators
Chasing the two word head term burns a year of effort on ground you will not hold.
The generic phrases are contested by companies with national content budgets, franchise systems with hundreds of locations, and resellers who buy the click and sell you back the call. None of them need to win New York specifically. They need to win everywhere, and New York arrives as part of the package.
A shop with three trucks cannot outspend that. It can outwrite it. Specificity is expensive for a national publisher and cheap for someone who does the work every day.
Specificity has three axes here. Borough or neighborhood. Building type, which in this city means brownstone, prewar walk-up, postwar elevator building or new construction. And the problem itself. Combine two of the three and the field thins out. Combine all three and you are often the only page that answers the question.
None of that is a reason to be pessimistic. Head terms convert badly anyway, because someone typing a generic phrase has not decided anything yet. The person searching for why a radiator bangs in a prewar walk-up has a specific problem and a specific building.