I don't think there is much that needs to be said about Slyman's. You just have to go! Giant corned beef sandwich = very happy belly. Best in CLE, best anywhere! Took my brother-in-law here yesterday. He's from NYC. He was impressed!
TIP: Try to go early to avoid a line and a wait. If you're doing takeout for lunch, sometimes the line is even longer than people waiting for a table. I noticed that people waiting in line when we first sat down just got their to go order as we were getting ready to leave.