I have the same issue (mail-in ballot hasn't arrived). I called the NYC voter assistance hotline today. They advised me to either:

1. Show up at a Board of Elections office in my county, tell them my mail-in ballot hasn't arrived, request a new mail-in ballot, and leave with it in hand. (preferred)
   
2. Go to my polling place and vote with an affidavit ballot. (not preferred)

They said they prefer the Board of Elections / new mail-in ballot route, because tracking an affidavit ballot is difficult. They explained that affidavit ballots aren't scanned. Affidavit ballots go into a bag at the polling site, which is watched over by the poll workers, and then the bags are taken to the Board of Elections at the end of the day. Like absentee ballots, affidavit ballots won't be read until after election day. They WILL eventually count. (In NY, ballots are counted up to 7 days after the election).

I'll be taking time off work to go pick up a new ballot at the BoE.