If you told us where you live or added your location to the thread title you'd have a lot better chance getting a geographically useful answer as steel (or any material) can vary a lot by locality.
I recently moved away from my old suppliers of 35 years in Central NY to NW NC so I had to start from scratch finding suppliers of all kinds.
I'm getting ready to start cutting steel for a couple of smokers so I opened a cash account at a supplier in Winston-Salem, After a little back and forth last week I got a quote of $217 for a 4x8' sheet of 1/4" hot rolled steel picked up from their dock. Depending on whether you get priced by square feet or weight that works out to around $6.78/SF or about $0.67/lb. Seems fair to me for my first order. And we've already established that we'll discuss adjusting my discount rate again once I establish a purchase history with them.
Very often all you need to do to get a discount is to ask for one..... One thing's for sure, though. You won't get a discount from walk in cash sales pricing without asking for it and likely will want/need to open a either a credit account or a COD account so that they can track your pricing history, too. It's a lot easier to get a discount if they have your prior discount history to refer to as opposed to having to haggle every time you walk in or with every inside salesperson in the place. And once someone gives you a better discount that generally becomes the minimum discount going forward as sales folks generally refer to the last discount given when pricing up a new order.....
In short, calling in and saying something like "Good morning, this is LanceR account number1234 and I need to place a steel order for pick up later this morning....." is a lot more likely to get you better pricing than walking in the door cold turkey.
I'd suggest starting with asking about opening a COD account. If nothing else it gets you on their mailing list for discounts, sales, demo days etc. And it is worth noting that metal prices can be pretty volatile. If you get a good price quote today it likely won't be good for more than a few days so don't assume that today's quoted price will be next week's or next month's price.
Good luck and thanks for a great question that a lot of folks have surely wondered about. Please check back and let us know how things play out so others can benefit from your experiences.
Best regards,
Lance