My 3 year old loves the museum of natural science. He could spend an entire day in the dinosaur area.
Zoo if you get there when it opens (beat the heat and the cluster **** the parking lot turns into).
Children's museum
Aquarium, but go into it knowing it's not the worlds best aquarium. That said, it still has fish if your kid likes them (mine loves them). We'll typically walk through the aquarium, walk to Post (pretty cool food hall with a rooftop terrace) for lunch, then back and walk through the aquarium again. Not nearly as good as, say, Texas State aquarium in corpus but can be fun if you set expectations.
Lots of parks and kid friendly restaurants.
The Jurassic world exhibit (haven't been personally) is going on in Katy right now.
The Marq-E (I10 west and 610) has a rotating exhibit. Right now it's called sloomoo, looks like slime related, but haven't been to this one so not real sure