It's no mountain, but
Enchanted Rock State Natural Area (or "Erock" as many of us call it) is a unique, must-see attraction. It's a pink granite batholith and you can hike to the summit and around the base of the main dome and its sister granite domes and "peaks". If you rock climb, it's a terrific spot for that too. It's fresh on my mind because Justin and I are currently in Fredericksburg, staying the the Hangar Hotel -- a place we visit several times a year, and especially around this time of year (holiday lights and aviation, since the Hangar Hotel is on the Gillespie County Airport and we're aviation as well as outdoors enthusiasts.)
Fredericksburg is a wonderful town to check out. Really, any of the Hill Country towns are (Kerrville, Bandera, Llano, Marble Falls, Burnet). Of course Big Bend is a must-see, though it took us years to get ourselves out there!
I love Colorado. Used to go there at least once a year, when I still had family living there (near Redstone, CO). Rocky Mountain NP has a special place in my heart and I've been lobbying Justin to take me back there soon. I want to do an early summer trip and, eventually, also a snowshoeing trip.