ORIGINAL: MinnFlyer
bigedmustafa had some great advise.
If you want to keep your field, show the city counsel that your club is an asset to the community - FIRST by forming a club. Keep the non-AMA members out. Now I am not a big proponent of the AMA, but when you're dealing with politicians, showing them that you are responsible (By belonging to a nation-wide organization AND having insurance) goes a long way.
Aside from big Ed's suggestions, talk to your local schools about giving lectures on basic aerodynamics. The kids love it, the club members love it, and it's one more feather in your cap if and when you are confronted by the city.
That's more good advice, MinnFlyer. We work with schools and cub scout/boy scout troops on a regular basis as well. Working with kids' organizations and putting on special events for scouts further enhances the club's public profile. Your club shouldn't be shy about building a file or display book with photos of these events, thank you letters from participants, and whatever other positive publicity you can generate.
If you walk into a city council meeting with a thick binder full of thank you letters from school teachers and photos of cub scout troops having fun and learning out at your field, it's going to help put one homeowner's complaint about noise in better perspective.
Do good works in your community, catalog those good deeds, and march them out when your club gets hassled.