Ian - I live in Staten Island so for us Newark wins hands down. LaGuardia is the closest to Manhattan (about 8 miles) BUT, it is the worst of the 3 airports. LaGuardia is well known for flight delays and other problems and, they don't handle a lot of International flights. JFK is about 15 miles from Manhattan and Newark is about 20 miles from Manhattan.
Price-wise, LaGuardia and Newark are almost always cheaper than JFK. Regardless of the airport you select, be ready for traffic and lots of it. ESPECIALLY during the holidays.
In fact, NYC is so bad during the holidays we have what is known as Gridlock Alert days. This is where the MTA (Metropolitan Transit Authority) adds more trains and buses and urges people to take mass transit to help ease the congestion. Even though the airports are physically close to Manhattan, figure it's going to take about an hour to get from the airport to your hotel in Manhattan.
Hope this helps in your decision making.