You should get involved in a Stay at Home Playgroup. I am the assistant organizer of a group that does activities in the Garland & Mesquite area. There are groups all of the Metroplex, so go to meetup.com and search for a group in your area. If you are close to Mesquite check out our group: http://playgroup.meetup.com/467/
Our group has 3 or so playdates a week, with one specifically for pre-walkers every other week. Our members always come up with different and usually inexpensive ideas to keep our little ones (and ourselves) occupied all week long. Other groups are not as active, while you may find one that is more active. If you are not interested in a group, here are some of the activities we do:
Mall playgrounds: Galleria, Frisco, Mesquite, Willow Bend, and even North Park has ducks & turtles to look at.
Baby storytime at your local library or bookstores.
Dallas Arboretum: free passes available at Dallas Recreation Centers. During the Spring & Fall they have Mommy & Me MOndays & Tiny Tot Tuesdays. This includes face painting, kindermusic, a petting zoo, and much more.
We often take my girls to local airports to watch planes (they are a little older though).
We've taken them to the Rain Forest Cafe to look at the huge aquarium and 'pretend' animals. Eat lunch before, try a dessert there, then go discount shopping!
I hope you find this helpful... I love our group and my girls love it too. I cannot tell you how many wonderful friends we've made just in the short 7 months we've been members. These groups are such a great resource so I hope you decide to become a member of one.