Hi. You can hang fliers for free at all Starbucks locations as long as you're not selling anything. I put up fliers for my son's preschool there with pull-off tabs at the bottom and I know people took them. I know in Irvine, the community centers will only post city-sponsored info, but it's worth a shot in other cities.
Also, I run a free website for Orange County moms and I allow businesses to advertise at no cost on the first of every month. Visit http://oc.citymommy.com to check it out! You can post every month on the first. I do have paid advertising options available as well. I know you can't spend money on advertising, but maybe we can figure out a trade where we advertise for each other.
As for handing out fliers at a park, I probably wouldn't really pay that much attention to it and don't think it's the best way to go.
Send me an email when you have a chance!
K. AT citymommy DOT com