Krawler, I do a google search for here and get 5 shops that sell metal
searched, metal supply.
I do one for Cleveland and come up with recyclers, foundries,brokers etc.
I would suggest calling your welding supply store and asking them. You are correct, they hide them there in Cleveland, seems if you are not buying a train load you are not buying steel.
I know there will be a place in the industrial business area of your part of town, too many businesses, welders, and fab shops need them to be close.
It may just take a search.
I found that getting to know one of the counter guys a bit helps, I do not go at opening, or during peak times, I go at a slack time and chew the fat a bit. I have been directed to good deals, had them hold something back for me, and get a bit of advice here and there because they know I am not a professional, just a home fab guy, and I always greet them with a smile and listen to them bitch about their jobs, customers, or coworkers.
I go and target my purchases, I make a list and hit up the remnant table, when I get the stuff to the counter to pay, they ask if I found everything ok, I pull my list and say, you know I need a piece of such a plate so big by so big to cut a few parts from. or a piece of such size 2x2 tubing to make some spring brackets from. I sometimes get them to go and get me a piece because they know I am not that professional, but just a guy like them saving money to do some hobby fabbing. Plus I show off my bumpers and stuff to them and they like that.
Counter guys control your purchasing power, so treating them right gets results, they are constantly having to deal with guys who are in bad moods or just pissed off and having a face they can depend on to joke a bit and make light with them is always a huge help.