Check out your local paper for free or frugal family entertainment. Here there is a weekly Pennysaver that comes once a week (it's free). It lists what is happening and puts it into separate sections. I usually end up just reading the section aimed at kids anyway. You can learn about different events at the library, free concerts at the park, new programs at the nature center, group bike rides, etc.

It also has coupons you can use if you eat out.