Historic and fabulous!
To begin, if you are looking for luxurious, modern, high-end details, don't go to the Menger. If you are looking for a charming hotel with character, history, and charm, the Menger is your hotel!
I spend a week there this month and had a fabulous time. The rooms in the 'historic' section are unique. The four poster beds, the old fashioned bath, the shuttered windows, all add to the charm. Yes, the bathrooms are a little old, and showing their age, but that is the point, right? You are looking for a hotel with some history, not a cookie cutter room.
The on-site restaurant is fabulous. We had breakfast their two mornings taking advantage of the generous buffet. The eggs were cooked to order, omelets on request, fresh fruit, breads, anything you can ask for. The wait staff is old-worldly and gracious.
The location is perfect. Right next to the Alamo. Two blocks from the conference center and two blocks from the River Walk. We were two ladies alone and had no fear walking the neighborhood in the evenings.
Try the Menger, you won't be disappointed! 
(P.S. Tell the spirit of the lady on the second floor I said hello! :))