High Rise Apartments in Houston Galleria: Dominion Post Oak Post Oak High Rise is a 230 unit skyscraper located in the Galleria area of Houston, Texas. Some of the many wonderful amenities tenants enjoy at the Dominion Post Oak include concierge service, a luxurious clubroom with media center, conference room, fitness center with an outdoor lap pool on the 6th floor above the garage, resident business center, and much more.