I always take our guests to have a snack in the lobby bar at the driskill and enjoy the old world charm of the lobby, the stained glass light in the middle of the floor, the marble, the wood paneling.
reminds me of many classic old hotels that are landmarks .. (many of the CP hotels come to mind that might now be Ritz Carltons etc.)
That said, I stayed in the hotel only once when visiting Austin and have to say that the rooms were a little small and dingy in comparison with what you'd find in a newer modern hotel. It's a fun experience to stay there .. and you are right downtown in the action so no complaints about that... but it would not be the place I would stay for every visit. You should do it once, and perhaps for a romantic stay .. or just for the experience
Remember to ask about the historical note from the lobby when you check in... you'll get a sheet that talks about the history of the hotel ...