You'd need a place near the equator, preferably unsettled but still politically stable. A mountain would be nice to shorten the length, but mountains are difficult.
For my internal fantasy I settled on Ascension Island, part of a British Overseas Territory, at 7.5° South.
It's not natively settled, the only people there are for work, military, spooks, space agencies for tracking and telecommunications. With the arrival of European explorers there was an ecological extinction, mostly the island seems to be barren.
And the name, of course, is perfect for a space elevator fantasy.