Spider Plant in kitchen: mold problem

White mild, a.k.a. saprophytic fungus is not going to hurt the plant, it just looks bad.

Remove as much mold as possible from the surface of the soil, make sure the drainage is good enough and try less water. Keep the plant in an airy space, if needed try a dehumidifier in the room as well. NYC is relatively humid, even for long stretches during winter. Additionally if you have steam heat or the plant is near or in a kitchen where a fair amount of cooking or water boiling takes place, you are building humidity.

If all of that fails, try repotting with fresh soil and invest in a new clean pot. As long as the plant is healthy, it's not likely you need to toss it.

I don't love the plant enough to go through that much work. I'll try the surgical removal of the mold and water it less I guess. I think I water it once a week (if slightly less frequent).