If you want a cheap flight from Exeter 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.
You can expect accommodation prices to be higher at this time of year too. Last-minute deals do crop up, but it's best to book everything in advance to avoid disappointment.