I lived in Houston for years, twice. Including in the immediate Galleria neighborhood.
I would not even consider going to Galleria unarmed.
Similar to the N.O. French Quarter, the crime "news" and statistics are "managed" to promote continuing business. The Galleria is a criminal magnet, with its many wealthy unarmed foreign tourist-shoppers. Galleria is full of everything from pickpockets, hookers, purse thieves, to the occasional armed robber; ESPECIALLY THE PARKING LOTS.
I sugggest for you to treat it like the F-Q. No purses, exposed cellphones, expensive jewelry, inattentiveness to suroundings, etc. Remain very aware entering/exiting vehicle, walking through parking, & while "trying-on" clothing.
H.P.D. encourages legal CC by honest citizens. Don't be afraid to talk to the guys & gals in blue. They're not the NOPD and are generally courteous and informative.
Remember, O.C. of handguns is verboten. Take care to keep your weapon & b.u.g. concealed. Pulleeeze, Ladies, no "purse carry" unless you really know what you are doing.
Also, almost every store in Galleria has similar stores in other Houston area malls, which have the same items at much, much lower prices. Very few Houstonians actually do routine sopping in the Galleria. It is a great place to people-watch, including girl-watching !
Enjoy your trip. P.M. me for restaurant recommendations.
leVieux
How was your trip to H-town ?