J.R.
All of these things are free: the city libraries have story time usually MTW around mid morning (check their websites), mine love to go to Petsmart and look at the fish, hamsters, birds, cats etc., Celebration Park in Allen is great for the summer time because they have the park play area and the sprinkler park, Towne Lake in McKinney is great for feeding the ducks and fish and playing at the park, and the soccer fields are a great place to fly a kite on a windy day.
These things cost but most are reasonable: the Dallas Aquarium, the Dallas (its fun to take the Dart Train and then they don't have to be in their car seat) and Ft. Worth Zoo, the Wiggles Play Center in Frisco,& Sharkarosa Ranch (in Celina I think).
Also watch for seasonal events: Thomas the Engine is coming to Grapevine at the end of March first part of April, McKinney has the Trout Fishing Derby in February and Allen's is in May, the Pumpkin Farm in Celina makes a fun day before Halloween, the Plano Hot Air Balloon Festival in Sept.& the McKinney Christmas Parade.