Found these guys via a Google search for "Cleveland Taxi" and they turned out to be fairly efficient and responsive. I used them over the course of a couple of days shuttling back and forth from my hotel in Beachwood to our company offices in Highland Hills. If you can schedule ahead, do so. The wait can be anywhere from 15-45 minutes though -- allow yourself extra time on snowy, stormy days.
Also - make sure to pick up your calls once you've gotten off the phone with the dispatcher. Chances are, the cab driver assigned is calling to confirm and if you don't pick up you're listed as a "no show" and abandoned.