Costa Rica only has 2 international airports: the capital San Jose served by most airlines and Liberia which mostly caters to tourist charter flights and also has limited commercial flights
The main places into Costa Rica right now are LA, Houston, Miami, Orlando, Atlanta, New York, Boston, Toronto and I am sure there are a few more that people will post
Check skyauctions.com they have auctions for airfares and if you click on the link at the bottom it shows how much more you pay from the list of around 100 cities in the US
The cheapest way to get to Costa Rica is usually to take a cheap airline to one of the southern cities and then find who has the best fare from there.
I think TACA has a promotion to Central American this month for around $500. In March I got a flight to San Jose from Boston for $342 on American and last fall American had a flight from Orlando for $122 even though it stopped in Miami(the flight from Miami was $199 at the time)
Lastly depending on where you live there are cheaper 1-2 week charter flights November-April. Call the local charter company and ask what date they start to fly to Costa Rica and usually there are some good deals in the first month before Christmas
At any given time there are better deals available from some cities. Pick your city and 2-3 that you can get to cheaply and then compare the prices. Be prepared to take the train from Ft. Lauderdale to Miami sometimes for a $100 savings