What is the IRS mailing address for an installment payment if I'm in Texas?

Per the IRS, all individual taxpayers who mail Form 9465 separate from their returns and who file a Form 1040 with Schedule C, E, or F should mail their Form 9465 to the address for their state.

The address for Texas is: 

Department of the Treasury
Internal Revenue Service
P.O. Box 69
Stop 811
Memphis, TN 38101-0069

Is that the same address for the actual payments that are mailed in?

No, the address is different.  

For other payments, depending upon which type of form you file, the address will vary.  Please see this link from the IRS for more details on which address would be used based upon the type of form filed.