If you're not familiar with Cleveland, may I offer that everything in Cleveland is 25 minutes from everything else. Fire food and drink at Shaker Square is actually only 13 minutes from that big pile of hotels in Beachwood.
Spice is the restaurant that I'm currently recommending, where by "currently" I mean since they opened a little over a year ago. It's only 26 minutes away. It's also a fun to be in a neighborhood like Gordon Square. You could see a movie, a play or some live music or go to a bar, coffee shop or ice cream parlor as part of your evening. And you could walk.
Even if you're only interested in dinner, Spice is the best restaurant in Cleveland right now and it's only an extra 15 minutes of driving.