So, yeah, before we start, let's talk a little bit about St. Petersburg. It was founded by Peter the Great, who was basically Russia's superhero tsar, using his power to modernize and industrialize the huge country.
While killing and basically enslaving a whole bunch of people in the process, of course.
But in any case, at the time when Gogol is writing, St. Petersburg is Russia's capital: home to the tsar, seat of government, and cultural and artistic center of the country.
This is why many of the story's realistic touches make perfect sense. On the political side, we get Kovalev's totally reasonable decision to move to St. Petersburg to push forward with his civil service career—which, yeah, if you wanted to be in national politics in the U.S., you'd move to Washington, D.C.
And we get his equally sensible habit of walking around Nevsky Prospekt every day—that was the big street where all the fancy people came to see and be seen.
On the cultural side, we get the funny juxtaposition of the grody barber trying to throw the nose into the river Neva from Isaakievskiy Bridge, the very first built across that river when St. Petersburg was first founded. And we also see that one of the confrontations between the nose and Kovalev is set in Great Gostiny Dvor, a huge fancy-shmancy shopping pavilion in the middle of the city.
So, "The Nose" is at least partly set in a real, 19th-century version of St. Petersburg. But there's more than enough weirdness to make us wonder what's really up. Sure, this is a St. Petersburg with all your tourist landmarks. But it's also apparently a St. Petersburg where people see a giant nose walking around like a person and think, "Celebrity!":
[It] began to be said that the nose of Collegiate Assessor Kovalev could be seen promenading the Nevsky Prospekt at three o'clock, or when a crowd of curious sightseers gathered there. Next, someone declared that the nose, rather, could be beheld at Junker's store, and the throng which surged thither became so massed as to necessitate a summons to the police. […] Next, word had it that the nose was walking, not on the Nevsky Prospekt, but in the Taurida Park, and, in fact, had been in the habit of doing so for a long while past, so that even in the days when Khozrev Mirza had lived near there he had been greatly astonished at the freak of nature. This led students to repair thither from the College of Medicine, and a certain eminent, respected lady to write and ask the Warden of the Park to show her children the phenomenon, and, if possible, add to the demonstration a lesson of edifying and instructive tenor. (2.136-138)
Here, suddenly, our little tour of the city turns into a crazy paparazzi-off as everyone tries to get to the latest place where the nose is supposedly hanging out. And just check out how many actual real-life places get name-checked in that passage and sucked into the story's dreamscape mirror version of the city. Here's our question: do all these real places make the setting seem more or less real?