If you want a cheap flight from Memphis to New York, you've got zero airlines to choose from.
New York La Guardia Airport is just one of the airports in New York. If you're not set on a specific airport, try changing your search from New York La Guardia Airport to New York to see a broader range of flights – they might be cheaper.
Keep your eye out for flights
If you're planning on going to New York during this time, you could take a look at other airport options. Or you could try to get a last-minute bargain.