Cleveland RTA:
Greater Cleveland Regional Transit Authority
It's not exactly a "subway"....it more of a "light rail" service that gets you from the suburbs in to downtown.
Mind you, our downtown is not large...it's completely walkable...there are also trolleys and buses that run throughout downtown that will get you wherever you need to go.
RTA's website DOES have a trip planner on it, so you can plug in where you want to go and from where and it will tell you exactly what bus/rapid/rail to take.