At this time, we do not know who Elizabeth Houston/Huston's parents were.

I need help with research.... There are clues:

• She named a son Thomas Wilson Neeley.  There is a Agnes Wilson married to James Houston.  This family also has ties to the Bakers. Two of Elizabeth's daughter's married Bakers. There were Houstons living in Sangamon Co near Phoebe Neeley Baker on the 1850 census. I haven't checked earlier.  
• Sangamon Co., Ill - need to check Probate Case for John Huston Jan 31, 1842.. Estate # 477  and a Jacob Neely 1833 # 136 Illinois Regional Archives Depository Lib 144, University of Illinois at Springfield, One University Plaza, MSBRK 140 Springfield, Illinois 62703-5407; phone 217-206-6520
• Elizabeth's son Houston Neeley had lived in MO. where there were other Houston relations....   need to check St. Claire and other counties in  MO.
• There were some Houstons in the Pike Co., ILL area... such as Sangamon Co, Ill.
• Alexander Neeley had land transactions with a Robert Houston on the New River (VA)... I believe he also had land transactions with a William Houston?
• A Neely female married a Houston at Manskers Fort, TN. 
• A John Neeley had been involved with a Houston girl in a law suit in VA...
• Houston, Neeleys and Cloyds, James McGavock intermarried in VA..
• Samuel Alexander Neeley was married to Elizabeth Montgomery, sister of Catherine Montgomery Bledsoe. Their family settled near Houstons in KY.     Wm Montgomery settled with father and brothers near Hustons on the headwaters of the Green River.   Benj Logan's Ft. St Asaph within 29 miles of Hustonville Ft in Lincoln Co Ky.   There was a James, John, Samuel and William Huston of later Bourbon Co. Joseph Houston of Pa came to KY with men in 1776 founded Hustons station, now Paris KY.   Samuel and his father Peter from NC settled near present day Paris.  James Houston b. 1796 in Iredell co NC m. Nancy Alexander they came to KY in 1793  Stephen Houston, Isaac Shelby and Wm Reed, Jacob Spears, Robert Barnet and Wm Warren had land along new road from carpenters to Danville.  There was an Elizabeth Montgomery in Clarksville, Montgomery co 1794. Col. John Montgomery was in Eddyville Ky.  Archibald Huston near Lexington was from Mill Creek Valley in Augusta, later Rockingham Co. VA
• Of course, there are family stories that she was a cousin to Sam Houston.  They did settle in Tx close to Huntsville.