"The Far King", a novelette by Richard Wilson, first published in Isaac Asimov's Science Fiction Magazine, March-April 1978, available at the Internet Archive. Does any of these covers look familiar?
The building is called the Mile-Hi Building; the bar is called the 5280 Club (the number of feet in a mile):
It was ironic that Ann Bagley got mixed up with a bunch of extraterrestrials in a night club at the top of the Mile-Hi Building in Chicago. But maybe it was inevitable. She was the daughter of the minister of a flock in a place like Zion, Illinois, home of the ecclesiastical fig newton, only it was a smaller place. I won't name it here, or name him. Ann Bagley or, as she was later called NoNo McCanless, is not her real name.
[. . . .]
I'd spent many years in the Mile-Hi Building, a day visitor among aliens from worlds unknown to our space explorers, when Ann Bagley came in one cold night. I scarcely remembered her as she stood at the door, cold from the wind and wet with snow, seeking shelter denied her by the YW, overbooked that New Year's Eve.
"What made you come here?" I asked.
She was looking around the 5280 Club in amazement, as well she might. It was not yet the dawn of interplanetary, let alone extrasolar, commerce as far as she and most of the other people of Earth knew.
Boots the bartender welcomed her in his transuniversal way and said "What will be yours?" and I led her to a far booth, away from the stranger residents.
"I knew you'd gone to Chicago and I needed somewhere to stay," she said. "What is this place, anyway? Some kind of circus—theater?"
I explained that most of them had arrived at one time or another on the Midnight Shipment. They were traders, businesspeople, scholars. For starters, I introduced her to a few of them—they slithered, rolled, oozed, or floated over to the table. She met Mogle, who's a triped; Diskie, who disappears when sideways; JorenzO the Black Magician; and Lopi of All-Planets Films. She was polite to them and they to her; she was taking it well for a person who had expected to spend that night at the YW. She also met Dan and Joe and Keith and Frank, Sam and Moe and Leif and Hank: a handful of Earthlings who, like me, had gained entrée by accident or because the aliens needed them in their commerce and gave them guest privileges.
Diskie is the 2-dimensional being:
NoNo's notebooks were private, she thought. She didn't know about Boots's attenuated pseudolenses which could snake across the room more invisible than spiders' strands to see what she wrote.
She didn't know about the talents of Diskie, a two-dimensional Slivian. Diskie looks like an oversized coin under a foot in diameter. Because he has no third dimension he's weightless and can hover at any level. And because of his lack of substance he can go through things or beings, or stay inside them. When he's not on end he's shimmery, like a silver dollar with a big face on the obverse that changes at his whim from terrestrial to extrasolar. On the reverse of his coinlike body appear and disappear mottos in English, which is the bêche de mer of the upper reaches of the Mile-Hi Building: Thin is Beautiful, Tomorrow the Whorl, Absorbed by Another, or The Inside Story. Diskie wasn't born or hatched, he said, he was minted; and when he entered NoNo it was in an asexual way. Thus he too was able to flesh out the story I might have called Inside NoNo McCanless.
