At the southeast corner of the capitol grounds is Texas's oldest state office building, the 1857 General Land Office. At present the building houses the visitor center for the capitol. It's a curious structure and looks a bit out of place with its Romanesque-medieval style and mock crenelated towers. Also uncommon is the surfacing of the exterior walls -- scored stucco to imitate stone blocks. The short-story writer O. Henry worked in this building as a draftsman for the General Land Office (1887-91), and you'll find an exhibit on the first floor remembering him. He based two stories on his experiences here. Also on the first floor is a gift shop selling all kinds of books, decorative items, and merchandise commemorating aspects of the Texas capitol, and an information desk that is somewhat redundant. The second floor hosts rotating exhibits about some aspect of the Texas capitol.
Tip: The Texas Department of Transportation staffs an information desk on the first floor of the visitor center. If you're driving around Texas at all, you can pick up a state map and a helpful travel guide for free. The guide lists almost all the towns in Texas and tells what's of interest in each.