You file only a Cleveland city tax return. Your employer should have withheld the correct amount of Westlake tax, so that you are not required to file a Westlake city return.
In Ohio, you normally only have to file a return in the city you live in. It is not necessary to file one in the city you work in, if different. Your employer will remit withholding to the city you work in, but you do not file a return unless you're claiming a refund or your employer didn't withhold enough ( both highly unusual). The city you live in will allow a credit or partial credit for the withheld tax you paid to the work location city.