[pseudo3d]

Hempstead's looks like a Project 79 store. There are a number of them still out there--I know that Navasota still has the old WAL-MART on it (from circa 1980, after they switched from the "Western" font--no star!) last I can remember (which was earlier last year, admittedly). Caldwell does, though it has the new Walmart font, as with Madisonville. A bunch of Project 79 stores were shut down in the 1990s for Supercenters.

[BillyGr]

Are you familiar with the "Wal-Mart Cafe" (or maybe it was meant to be read "Cafe Wal-Mart") concept? The WM in Aston PA, which was built as one of the last Caldors in 1995, becoming Wal-Mart in 2000, had a very small snack bar by this name. It had a fancy black/tan color scheme and an interesting ambiance, almost like a Starbucks. Sadly it closed in 2005, and was replaced by a Subway, but that also has since closed. Now the store doesn't have a snack bar at all, and has a nail salon in its place. Not sure but I think the Subway was owned by an independent Subway franchisee, and closed because that chain really overexpanded in our area.

And what about an eponymous snack bar? The Norristown PA store (which was a Bradlees), when it opened in 2002, had a very generic snack bar with a red and white oval "snack bar" sign, in the font of most Wal-Mart decor from the 90's. This concept also didn't last, and was replaced by a Subway which remains to this day. I vaguely remember this concept also being at a Bradlees-WM conversion in rural CT where I went on vacation in early 2003.

Given that all the stores you mention started out as something else (Caldor, Bradlees) - perhaps all these snack bars were originated by the original chains and then continued (maybe remodeled or redone or such) when WalMart took over the locations?
I know that at least one or two Caldors and a couple of the Bradlees here had eating areas (one Caldor even had Nathan's hot dogs).

[pseudo3d]

I might venture a guess that the reason why they were generic is possibly due to the area: maybe franchising problems, zoning problems, reducing "Wal-Mart shock", etc.

[pseudo3d]

According to some tax documents I found, the Dickinson TX Wal-Mart (#570) opened with a Corn Dog 7, though only for the first year of operation.

[Hughes56781]

In a similar vein, how many Walmarts have a fast food other than Subway or McDonald's? I've found at least two in Detroit that have Blimpie (gag) instead, and another with a Dunkin' Donuts.

The Supercenter on Hammer Lane in Stockton, CA has a Charley's Cheesesteaks...

[Hughes56781]

The WalMart Super Center on Hammer Lane and Holman Road in Stockton, CA was built in late 2004, and originally had a McDonald's... It replaced one which was catty-corner, which I don't recall had a restaurant, although it possibly had a snack bar... Anywho, I remember the McDonald's closed in 2020, I'm guessing due to the COVID-19 pandemic, and about a year ago or so, re-opened as a Charley's Cheesesteaks...