The Alamo is definitely not worth the long trip. Someone from DFW area and to the SW of there toward Austin will offer suggestions.
Harsh. Brutal. Unnecessary. Worst of all, sacrilegious. You call yourself a Texan??
While I've driven from SA to Dallas and vice versa for two-day trips, I'll agree that it would be better to fly from Dallas to SA if you want to see the Alamo and riverwalk for a day or two. Southwest Airlines has reasonable fees and plenty of flights from Love Field to SA International.
If the Alamo is definitely on your list, I can help you with other things to do in SA. If, however, you stay in the DFW area only, I'll defer to the folks up there for the best ideas.