Houston has an excellent museum district, and I think the children's museum and the natural science Museum are the best of those. They are about three blocks apart from each other, so you could do both in a day, depending on how much time you wanted to spend. If you're looking for something a little more touristy you might want to go to the Kemah Boardwalk. If your family is interested in the space program, a visit to NASA and the Johnson space Center can be a great day.
I think the best barbecue place in the Houston area is Killens, but that's way out in Pearland and you may not want to go that far. I think Houston does steakhouse better than it does barbecue. And two excellent Brazilian style places are that I can recommend are Fogo de Chao and Chama Gaucha.
You might also consider spending the day in Galveston. Lots to do there on the strand, at Moody Gardens, and Schlitterbahn.