I am afraid it has been several years since I have lived in Houston and now when I visit I go to Path of Tea which is an Asian teahouse.
However, I have heard good things about Serenitea Tea Room in Sugar Land. I have been told it is pretty posh and great for special occassions. There is also this place out by Katy Mills called Cottage Charm which is in a Victorian house. I went there a few years back and it was kitchy. But, I heard that it got new orners and went uber-Christian (not my thing) and fairly soon afterward went out of business, so you might want to look into that. That is really all I can think of.
Hope this helps!!
update: I did a quick search and found this which looks like a place that kids would like - it is all Victorian and frilly and has a special kids menu and it looks like maybe some dress-up stuff. There are two locations.