When traveling out of NYC, do you have to get a covid test BEFORE coming back, or can you get tested when you get back?

The latest revised rules depend on where you have been, and can be checked at nyc.gov/health/coronavirus.  As for testing before boarding aircraft, that is up to the airline, but most have dropped that.

It depends on how long you were out of state. If it was less than 24 hours, you don't have to test or quarantine. If more than 24 hours, you need to test before getting on the airplane to return plus you have to quarantine for three days and take another test after returning. If that test is negative, you can end the quarantine. Otherwise, you have to continue to quarantine for another 6 days.

These are two different questions. One responder has given you the New York. The rule of the airline are entirely different. A couple of airlines are requiring COVID tests for international travel. As far as I know, none are requiring it for travel within the US. But you need to check your airlines website for details. 

For travelers who were out-of-state for more than 24 hours:

- Travelers must obtain a test within three days of departure, prior to arrival in New York.

- The traveler must, upon arrival in New York, quarantine for three days.

- On day 4 of their quarantine, the traveler must obtain another COVID test. If both tests comes back negative, the traveler may exit quarantine early upon receipt of the second negative diagnostic test.

i would ask the airlines about it

https://www.coronavirus.health.ny.gov/covid-19-tra...