Leestown was a settlement in what is now Franklin county on the Kentucky River about a mile north of the settlement that became Frankfort. It was established in 1775, the first Anglo-American settlement on the north side of the Kentucky, by Hancock Lee. The name was often written as Lees Town and it apparently never had a post office. It is now within the city of Frankfort.
From Jedidiah Morse's The American Geography (London, 1794)
Leestown is west of Lexington, on the eastern bank of Kentucky river; it is regularly laid out, and is flourishing. The banks of Kentucky river are remarkably high, in some places 300 and 400 feet, composed generally of stupendous perpendicular rock; the consequence is, there are few crossing places; the best is at Leestown, which is a circumstance that must contribute much to its increase.