If, like me, you are not blessed to have a free zoo near your house, here's what I recommend:
Get a zoo membership.
Really. True, you look at the price of a family membership and your wallet probably winces just a bit (or a lot). But think of it this way, say it costs about $85 (our's is $79) a year, you know you probably won't go even every week, but say you go at least once a month, going on my admission prices for 1 adult and 2 children plus parking, you're looking at spending roughly $20 ($3 parking, $7 adult, $5 a child) if you aren't a member. But if you are a member and go to the zoo just 5 times, your membership has more than paid off. PLUS, if your zoo is like mine, you probably also get discounts to special zoo events and a discount at the gift shop (if your zoo has one).
But say the zoo isn't your thing, try to find a museum or children's museum near your house and get a menbership. Generally these types of things pay off after 5-10 visits, that's less than once a month. Plus, once you have a membership you find you go to them more often. That leads to learning more and more quality time with your child(ren).