The best place would be off of Bainbridge Avenue near Veterans Blvd on the northeast corner of the airport. This gives good views of aircraft arriving and departing on runway 1/19. To get there, take Veterans Blvd west to Bainbridge (stoplight next to Wingate Hotel). Take a left down Bainbridge, and make a U-turn when you can. Look for an.....uh.....adult book store.....and hang a right, go to the end, and there you are.
There are no real good spots for runway 10/28.
Two of us (MSYTristar and myself) work on the airport, and can get up next to airplanes, so you won't see us out by Bainbridge, but you should be able to get some good looks from there.
Tom at MSY
"The criminal ineptitude makes you furious"-Bruce Springsteen, after seeing firsthand the damage from Hurricane Katrina