There indeed WAS a Sheraton in Jackson MS many moons ago. I am not sure when the Sheraton brand left town, but I can confirm that in the early 1970s, the motor inn at I-55 and US Rte 51N was a Sheraton Motor Inn. That property stayed a Sheraton for at least two decades thereafter.
It had 100 rooms, then expanded to 180 rooms, and was sort of on Northside Drive near the intersection of Manhattan Road.
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Then, fast forward a few decades and there was a SHERATON REGENCY at 750 N State St downtown. That had about 250 rooms. This property was converted, it appears, into the Jackson DHS & Adoption bldg some years later. (Must've been one hell of a crappy Sheraton.)
In any case, I hope this info has been helpful.