In southern Louisiana, reasonably high ground is any place where the water line is below your knees.
No matter how I try, I always end up with too much.
And I’m totally stealing that line you totally stole from Shakespeare.
Forgive me for asking the obvious, but if you take any two and only two points on a map, can’t you connect them with a straight line? 
Any three whooshes make a plane!
Don’t you need wings?
We all need Paul McCartney.
If you draw a line from Cincinnati OH to Cleveland OH, you’ll find Columbus really close to the line and near the middle. Now, Cinci is on the Ohio River, which was a major thoroughfare back when Ohio (the 15th state) was the old old old west. And Cleveland was a port on Lake Erie. Good reasons for them to be there. AND Indianapolis, Columbus, Pittsburg, and Philadelphia are pretty much in a straight line too. I suspect the location of Columbus (Franklinton) was placed on a map before any buildings were erected there.
Columbus was established specifically to be the capital of the state, and it was deliberately put in the middle of the state for convenience.
Richard de Mille, in one of his books about Carlos Castaneda, adapted it best, in my opinion. In writing about people playing with psychedelic mushrooms, he observed that
Now lets not exaggerate… Around here reasonably high ground is anywhere that doesn’t squish when you walk on it during a drought. If it is dry during the height of summer, it is high enough to build on. 
As for New Orleans proper-remember the French Quarter did not flood during Katrina (pretty much has never flooded). It is built on the old natural river bank. Anything away from the river was swamp up until the city decided to drain the swamp and build farms.
Columbia, South Carolina was sited where it is for the same reason. Something about capitals named after Colomb. 