Just to clarify, the Alamo interior is closed at night and you cannot tour the building then. But the spacious and well-lighted plaza in front of the Alamo is open and the front of the Alamo is well-lit. Many people seem to enjoy stopping by at night to look at the building, read the historical displays out front and chat with the security officers. It is close to the Riverwalk and the Dennys and is well worth a visit.
When I walked from my hotel on the Riverwalk to the station in the early morning to catch the Eagle to Chicago, I made it a point to take a brief detour on the way and stop by the Alamo for a last look.