Besides the huge Galleria..well it depends really on what type of stuff you like.
There is the Rice Village which has Urban Outfitters,a lot of boutiques,an express,gap,victoria secerts etc.
Then there is Westheimer/Montrose area. If you go inbetween Dunlavy and Montrose on Westhiemer there are a bunch of vintage/resale shops such as Taxi Taxi, Leopard Lounge, and Buffalo Exchange. And on Dunlavy right by Brasil's (an awesome rest/coffee shop)there are a couple of boutiques one of them is called Eden.
Then there is Memorial City mall near Memorial. The only thing I go there for is Forever21 they also have a bunch of other stores but the place is constantly packed with stay at home moms.
Other than that I do most of my shopping online. If I think of any other places I'll let you know. Good luck.
