Corky and Lenny’s was just “ok” when I visited a little over 10 years ago.
 
For a good deli experience try http://www.jacksdeliandrestaurant.com Jack’s Deli
I was last there in 2008. Great Matzoh Ball Soup and a decent pastrami sandwich
 
What I found fascinating is that there seems to be more Jewish Style Delis in Cleveland than there are in NY. 

I have had some very good breakfasts at http://luckyscafe.com Lucky’s Cafe in the Tremont neighborhood.
 
As for a deli, I have never been there, but know people who love http://www.roadfood.com/Restaurant/Overview/5072/slymans-restaurant Slyman’s.  http://www.corkyandlennys.net Corky and Lenny’s is pretty good, too.

Hey,  thanks for reminding me of Westside Market.  One of the best farmer’s markets around.  I’m gonna be in Cleveland this week and I’ll have to check out the Market. 

Sokolowski’s has good Deli AND Polish items. Don’t know if their open for breakfast.
http://www.sokolowskis.com/lunch.php http://www.sokolowskis.com/lunch.php

Luckys Cafe is great, best Mac and cheese Ive ever had, also excellent biscuits and gravy

Luckys Cafe is great, best Mac and cheese Ive ever had, also excellent biscuits and gravy

Glad to see another fan of Lucky’s.  I have had the mac and cheese and it is indeed great stuff.  But, I have missed out on the biscuits and gravy.  Next time.  Thanks for the tip! 

If you have the time, try to get to the West Side Market. The various jerkies at Csuchraj Meats are not to be missed.
 
http://www.westsidemarket.org/about.html http://www.westsidemarket.org/about.html

Cleveland is definitely a good roadfood city.  I like Slyman’s Deli a lot.  it’s just wonderful.

Been to both Corky & Lenny’s and Jack’s.  Liked Jack’s a little bit better, but they’re both good.
 
If you want to go beyond deli’s, between buffetbuster, wanderingjew, ChiTownDiner, and myself, we can recommend so many places you’ll be stuck in Cleveland for a month.  Say the word and let the avalanche begin.
 
Buddy