Knoxville, Tennessee is about halfway between these two points.
I am pretty sure your answer is the Arkansas river.
There are at least 4 cities named "Lafayette" in the United States, but I'm guessing you mean Lafayette, Louisiana, which is the closest of them to Natchez, Mississippi. The halfway point between Lafayette, LA, and Natchez, MS, depends on whether you take the fastest way (through Baton Rouge) or the shortest way (the scenic route). Using I-10 and US-61, the halfway point is just on the north side of Baton Rouge, on US-61. Using I-49 through Opelousas, to state highways 10, 360, 105, 1, 15/970, and 131, the halfway point is Simmesport, LA, right where you cross the Atchafalaya River.
White River City, Colorado is the halfway point.
Wood River, NE
Roughly, the halfway point it northwest of the town of Canonsburg, Pennsylvania.
neuseri river
The Ohio River.
Harrisonburg and Staunton, Virginia
Magnolia, NJ
The halfway point between New Hampshire (NH) and Texas (TX) is Salt River, KY.
The address of the Crystal River State Archaeological Site is: 3400 North Museum Point, Crystal River, FL 32629