Why isn’t Rochester on Lake Ontario?

Rochester’s downtown is located about 12 kilometers from Lake Ontario.  The Genesee River runs from Lake Ontario through the city and cuts right through the middle of downtown.  It struck me as odd that the downtown was located so far from Lake Ontario.  Other cities on the Great Lakes – Toronto, Buffalo, Chicago – are all located right on the lake itself.  I know that the Erie Canal was important to this region, but Rochester was incorporated before the Erie Canal came along.  So what’s up with the inland location?

According to my in-laws, Rochester was established along the Genesee River in order to capture the energy generated by High Falls.  What?  There is a giant waterfall in downtown Rochester?  I had no idea.