Any county clerk in Texas can issue the license, and it works in all 254 counties, so apply wherever the line is shortest. Fees vary by county in ways worth knowing, and one free course saves both money and time.
In Gillespie County, which issues from the Fredericksburg courthouse, a license runs $80 for Texas residents and $180 if neither applicant lives in Texas, since the state adds a $100 surcharge for out of state couples. Hays County (Wimberley and Driftwood) and Comal County (New Braunfels and Gruene) each charge $82. The license stays valid for 90 days from issue, and both of you must appear with photo ID.
Texas imposes a 72 hour wait between issuing the license and holding the ceremony. Complete Twogether in Texas, the state's premarital course, eight hours with free providers available, and two things happen: the $60 state portion of the fee drops off, taking Hays and Comal down to $22, and the waiting period disappears entirely. Active duty military carry their own exemptions. For a couple flying in Thursday to marry Saturday, the course is the difference between a wedding and a very nice party.
Texas accepts online ordination and keeps no officiant registry, so a friend can legally marry you; judges and clergy qualify as well. Whoever officiates must return the signed license to the issuing county within 30 days, a chore worth assigning before the toasts start. If one of you cannot appear at the clerk's counter, an absent applicant affidavit exists, though standing in by proxy at the ceremony itself is reserved for deployed military. And mind the calendar: a license collected in June expires before an October date.