The City has this detailed article about possibilities for independent candidates, and minor parties, in the New York city election of 2021, not just for Mayor, but for other positions as well.

The hostile 2020 ballot access changes do not apply to petitions other than statewide petitions. Not only that, in 2021, the legislature passed a bill cutting the number of signatures in half (for 2021 only) so a candidate for the general election for New York city citywide office only needs 3,750 signatures. However the 2019 bill moving the petition deadline from August to May does impact the 2021 city petitions. The petition deadline is May 25.