Palm Restaurant, The Home / Palm Restaurant, The Share: RESTAURANTBUSINESS BUILDER MEMBER Palm Restaurant, The Visit Website 6100 Westheimer Road Suite 100 Houston, TX 77057 (713) 977-2544 Visit Our Website About Map About The Palm has been serving the galleria area proud for almost 40 years as one of the premier steak houses in the galleria area. What's Nearby? Distance: 5 10 15 20 25 50 mi.