Ruggles was far and away the best place in town when I used to visit Houston regularly in the 1990s, serving South Western American cuisine. The menu is extensive, and there is a tendency to add one too many flavour to its dishes, but in general this is kept in check and the strong execution and good ingredients overcome any reservations. Service was good, and the wine list excellent.
@NjDimond Some options: Bull and Last (north), Harwood Arms (west) Dysart (v west), Delaunay (central). Or Ritz (if you fancy posh).