I think I've found it: the Chersonese.
Googling for "Cimon exile Attica" landed me in the Perseus site.
Andocides, in On the Peace says this:
Now take the days when we were fighting Euboea and controlled Megara,
Pegae, and Troezen. We were seized with a longing for peace; and, in
virtue of his being Sparta's representative at Athens, we recalled
Cimon's son, Miltiades, who had been ostracized and was living in the
Chersonese, for the one purpose of sending him to Sparta to make
overtures for an armistice.
Andoc. 3 3
The edition - Harvard University Press, 1968 - has this note:
A double historical error. （a） Andocides means Cimon, son of Miltiades. （b）...
Then, searching for "Cimon exile Chersonese", I found History of Ancient and Modern Greece, by John Frost:
About the same time the two great parties in Athens were reconciled,
and Cimon was recalled at the motion of Pericles, having completed
only five years of his term of banishment, which he spent on his
inherited lordship in the Chersonese.
This seems to confirm the Chersonese, although the book is from 1851 and the idea of Cimon being exiled for "only" five years is, from what I've read, somewhat debatable today.