If memory serves, Rita was initially projected to hit South Texas, and it ended up hitting the TX/LA border area.

A reminder of the damage caused by the 1900 Galveston hurricane, as it moved inland (note that it became a hurricane after it moved past Cuba):

http://www.islandnet.com/~see/weather/events/1900hurr.htm

Most accounts of the Galveston Hurricane of 1900 stop here and focus on the human tragedy that hung over the devastated city. Although the storm winds likely dropped below hurricane force shortly after the storm moved inland, the storm continued its destructive path into Texas, before crossing the southern Plains states and finally recurving to the northeast to pass across the lower Great Lakes. It eventually reached the Atlantic Ocean after crossing over the Canadian Maritime Provinces and Newfoundland on September 12-13.

Along the Texas coast and just inland, the towns of Texas City, Dickinson, Lamarque, Hitchcock, Arcadia, Alvin, Manvel, Brazoria, Columbia and Wharton suffered great damage and loss of life and property. Over half of the buildings in Houston were damaged. Along a path two hundred miles wide, wind and rain blasted inland Texas from the Gulf to the Red River Valley. The inland towns of Hempstead, Chapel Hill, Brenham and Temple were ravaged.