The museum was a separate building. The Alamo itself was reconstructed over the years (the facade is not original).

There's a string of other missions around San Antonio: a local told me they were more interesting than the Alamo, and that the city ran a free bus service to them and other tourist sites. One of them is still in use as a Catholic church: there's an arrangement between the US Park Service and the church that the latter maintains the active churches while the former maintains the grounds and exhibits. And they acknowledge that people lived in the area before the Americans tried to take over.