We live between Pittsburgh and Cleveland. Both zoos are great and there's lots to do in those areas. Erie and Akron (Ohio) both have smaller zoos as well.
However, the best zoo we've been to in this area is Columbus (Ohio) Zoo. If you are going when it's warm, they also have a waterpark. We are about 3 hours from Buffalo and 3 hours from Columbus, so it should be around 6 hours or less of a drive. It's a great city with tons to do. I highly suggest it for a weekend trip.