we lived in the area for 3yrs and loved it!
you can do the science museum for FREE

(you pay extra for parking, the movie, the planitarium,and one or two other things.. we never found it a problem to skip those things though there are sooo many things to see and do there.. also if you park on the forest park side parking is free)
the zoo is free
the art museum is free
and the history museum is free i believe
all located in forest park
you can explore the museum under the arch for free.. dont forget the jr. ranger program which is free to participate in! (it only costs to do the movie or go up in the arch)
I highly suggest hitting the city musuem for the kids they will LOVE it!!
http://familyattractionscard.com is a great place to get coupons for all things st.louis i think you have to register but its free to do so..
hope you enjoy!!