I have been unable to find any clinics that provide free abortions in the Houston, Texas area.
The clinics that do provide abortions, of which there are increasingly fewer in Texas due to state laws, will charge some sort of fee, though may offer free pregnancy tests.
You may wish to contact the following clinics:
Aaron Women's Pavilion/Texas Ambulatory Surgical Center
Address: 2505 North Shepherd, Houston, 77008. Phone: 713-880-3354; 713-774-9706. Toll Free: 800-392-6251.
Planned Parenthood Center for Choice
Address: 4600 Gulf Freeway, Houston, 77023. Phone: 713-535-2400. Toll Free: 800-831-6538.
The Lillith Fund is an organization that helps women with reproductive issues in Texas and can answer questions about Texas abortion laws. Their address: P.O. Box 684949, Austin, TX 78768.