How to entertain your kiddo on the cheap...

get to the library
join a parents/moms group (check meetup or search groups on facebook)
 look into what's going on at the area museums, attractions & parks
start following local bloggers, they'll post reviews and maybe host ticket giveaways
don't forget the malls & stores!  Most malls have a playarea and chain stores such as Home Depot, Michaels and Barnes & Noble will host storytimes and crafts