I've actually had really good luck doing something like this, not necessarily because I was trying to save money, but because travel plans changed and I preferred to be on the opposite side of the city. I've walked into United Clubs a few times, and after sweet-talking have managed to have the my arriving airport changed....

... I have only tried this swapping between JFK and EWR a couple times, and any chance I can find to arrive somewhere other than LGA.

The last time I wanted to do this, I got really lucky had a IAD-JFK leg that I wanted changed to a IAD-EWR. At first the agent was skeptical and told me I had to pay the difference in fare plus a change fee, but then she called the SHARES help desk and they walked her through how to do it for me for free! (I think in this particular instance there was a IRROP policy for weather in NYC though, even though on landing there wasn't a cloud in the sky)