There have been social media reports (#CityMD) of 2-3 hour waits at CityMD. (The above photo is from this morning around 8 as the line outside the 14th Street CityMD outpost stretched halfway down the block between Second Avenue and Third Avenue.)
Some knowledgeable/trustworthy sources online have reminded people about free city-run test sites. Find that list here. And this site has the wait times for NYC Health + Hospitals COVID-19 testing locations. And here's a list of free mobile testing units. You'll have to travel a little bit for this — none of the locations are in the East Village.
The city is reportedly expanding testing sites, distributing masks and giving away at-home test kits... though, as many people have pointed out in news articles on this winter surge: 20 months in, it shouldn't be so difficult to get a test. (And this article at The City reports: "De Blasio Shut Down 20 City-Run COVID Testing Facilities Ahead of Omicron Surge.")