It's hard to imagine a salary of $125k/yr being competitive for senior developers or directors in NYC, whether we're talking about a startup or a billion-dollar company.
Moreover, people capable of working remotely can participate in job markets (and benefit from their corresponding pay rates) not only in NYC but also places like San Francisco and Boston.
From a personal perspective, when job postings mention 'competitive' pay but won't establish a baseline expectation involving concrete numbers, I generally feel safe making the assumption that the salary on offer is on the low end of average; otherwise, mentioning it explicitly would be a great differentiator.
I purposely said $125k minimum since that is the lower bound of our Engineer IV salary band. What we pay for director-level is entirely based on experience (e.g. a master craftsman might make more base than I do as an SVP)
That said, it is possible that we still need to pay more.
> That said, it is possible that we still need to pay more.
It can't hurt!
One might also consider referencing a concrete salary band in the job posting. IMO, the cons from the hopeful employer's perspective (relinquishing some negotiating power) are far outweighed by the pros (setting correct baseline expectations as to both required skill level and average compensation for same).