What Building Is This In The Background? in Historic Houston Posted January 19, 2015 Yes, Conoco Building, my mistake. I have been reading up on Central Bank and had that on my mind. All these years I have been under the impression First City was razed; never knew it was still there, but I don't go downtown very often and can't do much sightseeing when I do. However, I'm having doubts that was First City, anyway. It appears to have multi-hued panels, First City was silver and squarish from this angle, I think. Possibly Houston House or whatever that building was called? Is that the Sheraton Lincoln on the left edge?