The Ft Worth Science Museum is fun. There are a lot of hands on exhibits, The children's area has a pretend hospital (with a nursery) and pretend grocery store and a water play area. I took my 1 yo to see the One Big World show at the planetarium this week...she loved seeing Elmo and BIg BIrd.
The FW museum is fun, we love it and we are members. But the Dallas museum is even better if you are willing to drive. There is a lot more hands on stuff and the children's area has some really fun and creative stuff for the kids. And as an added bonus, unlike the FW musuem, the dino dig is inside and out of the heat.
Let's Jump has a great toddler area and they allow mommy and daddy to play too. You have to call them ahead of time to check the general admission hours. You may want to do a "test run" on this place. The first few visits my little one sat in my lap and watched her brother...the noise of the bouncy stuff scared her.
The FW zoo is great, but it may be a little hot to enjoy that. The Keller Rec center has some discount tickets available.
It's pricey, but the Dallas World Aquarium is a really unique visit. I think it's over priced, but it is unlike anything I have ever seen around here. It's all indoors. And it ends with a view of manatees, something you don't see in Texas.
If you just want a simple party in the park, we are lucky to have some really nice ones. We enjoy Bear Creek Park...definitely bring some bread for the ducks. Johnson Road park has an area specifically meant for 1-5 yo. It also has no water to worry about. We also love the park on Keller Smithfield...but some of those slides are too tall for a 1 yo.