This Whataburger at 105 Dominik Drive is another restaurant that has been here for decades (though been rebuilt a few times). This is the closest Whataburger to campus and I've heard (and felt) like quality is a bit sub-par compared to the Rock Prairie Whataburger. In 1969, it changed hands from an unknown seller to Grace Dobson (wife of Whataburger founder Harmon Dobson), with the earliest reference in newspaper archives to this location in 1971. In 1987, Grace Dobson to Whataburger. It changed hands again in 1987 to Whataburger officially, which was about the time a rebuild of the store commenced, as a permit had been filed in 1986. Regardless, it was rebuilt again in 1996. This is what Brazos CAD says about the store, and that is correct--I had heard when I was a bit younger of a large fire at the store in the 1990s, and later I found a newspaper that said that it did in fact burn down in January 1996, with a "mobile Whataburger" serviced the area until the Whataburger reopened that spring. The store was No. 78 even in the Dobson days and it still is.
While it is the closest Whataburger to campus, for a brief time it was not as you could get Whataburger in the Sbisa basement, and with the revelation that they had a "mobile Whataburger" even back in the mid-1990s, it makes me wonder how much money a Whataburger food truck could still make on campus today. It was at this location that I realized Whataburger had subtly changed its logo.
Today, it has an all orange logo (formerly, the name was in black and there was often blue trim). Compare this picture (not mine!) to the store today. There's another blank lot nearby used for overflow parking. This used to be a Shell station (it was a Texaco prior to 2003) just about three years later when Texas Avenue started to widen, and demolished a few years later. Since then, nothing has taken its spot, but it provides excess Whataburger parking. It was one of the "Max Food Mart" stores that were in a lot of the Texaco stores at the time. The gas station at 1405 Texas Avenue I believe did not co-exist with the old Zip'N at George Bush and Texas, as the stores I remember converting around January 2003 (Eagle archives show the conversion of the store at Southwest Parkway and Welsh converting, and I think that was one of the first to convert), and by February 2003, the old Zip'N had been completely leveled.
Update May 2019: This Whataburger is scheduled to be rebuilt soon, and the Gumby's has moved out.