The newest is the Plattsburgh Airport, only 40 minutes away, it has 3 non-stop flights to Boston and flights south to Florida effectively replacing the Saranac Lake Airport for Keene travellers. Burlington is an hour and 45 minutes away has good service to NYC/JFK, but otherwise limited flights. Albany is only 15 minutes further away and has more airlines and more flights, hence better fares. If you are going to Europe, Montreal is a good bet because you can get non-stop flights to many cities in Europe, using the flights to Boston to get a connection to Europe is a lot shorter drive than Montreal.
Parking fees at all the airports are reasonable and it is free at the Plattsburgh airport. For a longer trip, if you can’t get someone to drive you, the easy way to get to the airports is a car service, Majestic Limo in Lake Placid serves Keene.
Plattsburgh Airport
Plattsburgh (PBG) has built a new passenger terminal and is served by two airlines. US Air Express, flies direct to/from Boston 3 times a day in about 70 minutes. Flights to Boston leave around 6am, 9:30am and 4pm. and the return flights to PBG leave Boston around 8am, 2:30 and 7pm. Fares are as low as $52 each way. US Air connections so it's possible to leave PBG at 4pm and be in San Francisco at 9:40pm with fares as low as $300. These flights make good interenational travel connections as well. The planes are 34 seat turboprops.
Alligent flies to Florida (Ft Lauderdale, Orlando and Tampa), but not every day. More recently, Direct Air started offering flights to Myrtle Beach and Ft Meyers. Fares for these flights are very reasonable. Parking is free. It is at the old Plattsburgh Air Force base, south of the town and it takes about 40 minutes to drive there from Keene.
The Adirondack Regional Airport, Lake Clear (SLK) is also known at the Saranac Lake Airport. Has Cape Air has service to/from Boston, with 3 flights a day on 9 seat planes. This airport is about 50-60 minutes away from Keene. So, I don't think this is very useful to Keene anymore now that Plattsburgh is closer and offering the same or more flights, better fares on bigger planes with better connections.
Albany Airport
The Albany Airport (ALB) is two hours south. It is served by 8 airlines and generally has the lowest fares of the area airports. It has non-stop service as far west as Las Vegas (on Southwest) and to a few destinations in Florida. You can even get to San Francisco with only one stop via Southwest Airlines. With 90 arrivals and 90 departures each day, it has flights to the major hub airports like JFK, Chicago, Atlanta, Detroit, Washington Dulles, etc. The airport web site has current flight arrival and departure times.
Burlington VT Airport
BTV is served by 7 airlines, including Jet Blue, and Burlington is the closest airport to Keene. The drive time is about 1 hour and 30-45 minutes. Using the Essex Ferry and the Crown Point Bridge take about the same amount of time. It has fewer flights and fewer non-stop destinations than Albany. Fares always seem a bit higher. It does have 7 flights a day to NYC/Kennedy and from there you can get the cheapest fares to just about anywhere in the world. Chicago, Detroit, Newark and LGA, Washingon, Philadelphia and Orlando also get direct service from Burlington. The airport web site has current flight arrival and departure times.
Montreal Airport
If you are heading to Europe, then using Montreal (YUL) means you get a non-stop flight. Paris, London, Frankfurt, Zurich, Amsterdam, Athens are all reached via non-stop flights. There are also many direct flights to the Caribbean and Mexico. Around 32 airlines fly from Montreal so fares tend to be good. It takes about 2.5 hours to get to the airport from Keene. The drive is not hard but use google maps to find the route and review the section of this website about the border crossings. Traffic in the immediate airport area can be very bad during the evening rush hour. The airport web site has good info on real time flight data, parking, etc.
Lake Placid Airport
The Adirondack Flying Service is a charter service out of the Lake Placid Airport right near the Horse Show fields. They will go anywhere but trips to places like Boston and New York City are common. You can get a price quote on their website. The prices are per plane, not per person. So, if you have a groups of 5 to 7 people, it can be very competitive with commercial airline prices. The airport is only 10 minutes from Keene and you get right on the plane without any hassle or waiting. I've used the service twice for day trips to Boston and to Hartford and it was great. They also do scenic flights around the area.