Akron, Kent, Case, Baldwin Wallace, Spire, Mount Union, Oberlin, Cleveland State, Youngstown State...Just try and get in contact with a coach or someone on their teams and most will give you times you can use the facilities. Kent was very good about it and even had public times a few years ago.
Even the Natatorium in Cuyahoga Falls has an OK track. Ashland and I think Wooster have facilities.
Just see who you can reach out too. You should be able to find something close.