If you have an idea when the house was built, or a name of an early owner, city directories are often a great place to start researching.
City Directories: Some early San Antonio city directories (prior to 1960) are available online through the library's subscription to Ancestry.com (Library Edition). This database is available, from a library computer, at all SAPL libraries. Ancestry can be found on our homepage under “Services -> Databases.”
If you think the house was built AFTER 1905, look up the address in the “Street Listing” part of the directory. Doing this will give you the name of the person living there, most likely the “owner.”
Keep working backwards in time until you hit the 1901 directory. (The Street Listing part of the directory didn't start until 1903.)
At this point you’ll need to research by name of the resident and see how far back that will take you. What you’re trying to do is go back as far as possible to determine the year the house was built by seeing when the address first appears in the directory.
Once you’re at a city directory where the family is no longer listed at your address (or not listed in the directory at all) move on to land/deed records.
The document below contains a short set of instructions on how to get to city directories on the Ancestry (Library Edition) database.