I do not like to photograph people, I try to avoid them at all costs
So, I always go to parks for nature shots. However, many parks do free concerts, or host triathlons and such. So they may offer some opportunities for you.
Also, Groupon is a great a place to find discounted prices for zoos or museums if have them in your area.
I live in Washington State and there is a water airport near Seattle, that allows us on the flight line for free to take photos, but you can't get any of the plane numbers, so that may be something that you can do.
Are there street fairs in your city that you can snap photos of? We have them here quite often and antique car parades as well.