If you're seeing yellow petals with various degrees of brown/maroon on the inside of the petals, try Rudbeckia hirta (varieties such as 'Autumn Colors').

I'd be surprised if it's blooming already though.

Sorry, I gave the impression I was seeing them now. I meant that I know I will be seeing them, since they come up every year. And I looked up Autumn Colors and that's not what they are. The petals are yellow, and the flowers are above my waist (I'm 6'). Though I think you're right, it is hirta, but maybe Indian Summer?

'Indian Summer' does not have the "brown/maroon on the inside of the petals" unless you are referring to the cone itself.

Cherokee Sunset?

Yet another mistaken impression I've given. When I said brown I was only referring to the eye itself. The petals are completely yellow. It's a big, tall, yellow flower with a black eye (I've only passed it in car so maybe the eyes are brown--there's such a thing as a brown-eyed susan,isn't there?).

Could it be rudbeckia triloba?

Here is a link that might be useful: Brown Eyed Susan

It sounds like you are referring to Gloriosa Daisy, which is a variety of Rudbeckia hirta. There will be daisies with solid yellow petals and a brown eye, as well as ones with brown markings on the petals in a mix. Rudbeckia laciniata, Herbstonne also meets your description, except it usually gets about 5 to 6 feet tall. It has really excellent foliage.

OK, now this is turning into a detective story. They have the exact habit of triloba: good spread, very upright, lots of blooms. But triloba petals aren't the right shape, too rounded. The petals are more like gloriosa, tapered and longish. But it's not gloriosa because there's no brown on any of the petals, just a profusion of pure yellow. (I also just asked the woman whose yard they are in and she said she doesn't know what they are.) Hmm, 'Indian Summer' maybe? By the way, please forgive my habit of speaking in the present when I'm really referring to a flower that won't be appearing until July. And I'm glad you mentioned laciniata. Those are on my list to get for the back of a bed.

Rudbeckia lanciniata may take over your bed, then your yard...and sleep with one eye open too :)

Gloriosa daisies are a mixture of bloom types. You will get some blooms that have brown markings, but usually, I get the most of the blooms that are a solid golden yellow with brown eye. Whether it's the one you're after....who knows?

aralia, that is news to me! I have had Herbstonne for a good five years now in good, fertile, well drained soil, and adequate moisture. Only last year had the clump gotten large enough to divide! I have never heard of this one being invasive, though Goldsturm most definitely is.

Aralia, you and I are in the same zone, so that's good to keep in mind about the cutleaf. Could there be something about your zone, DB? Though who ever heard of warmth inhibiting invasiveness? Another mystery!

The hirta varieties generally have hairy leaves.