If you are looking for a cheap parking, google dollar parking, MSY.
I am not a Dollar agent or something, but I just found, it turned out very cheap. On the airport, it costs 12 $ per day. For my 4 days' parking, it would have cost me 48 $, but with Dollar parking, I ended up paying on 34 $ (including 2 $ insurance)!
In today's hard economy, 14 $ saving is a big thing.