Word for the “fakeness” of extravagant places

Solution 1:

Given appropriate context, superficial could convey such a property.

not thorough, deep, or complete; cursory. "he had only the most superficial knowledge of foreign countries"

lacking depth of character or understanding. "perhaps I was a superficial person"

(From Oxford Languages, from the Google results)

While it can be used to mean various things, I think if you described a city as superficial it would usually be understood to imply that, as you say, "the surface-level extravagance is hiding something". However, depending on the specific instance this could be misunderstood (for example as describing the people rather than the buildings).

Solution 2:

While I don't think there's a perfect word for you situation, one that comes close is "tawdry" looking bright and attractive but in fact cheap and of low quality. (Cambridge)

"Gaudy" unpleasantly bright in colour or decoration is also applicable and also negative.

Others that may be useful in forming a picture are "gilded" or "gold-plated". The impression I got of Vegas was gold-plated fibreglass -- shiny but not even solid. Continuing in a similar direction we have "thinly-veiled" but thinly-veiled what? A casino may be a thinly-veiled attempt to extract your money in the guise of entertainment, but the ambience isn't quite that of a thinly-veiled con. A veneer of sophistication (or of something similar) could be a useful phrase too.

An (almost) applicable description is "Little expense had been spared to give the impression that no expense had been spared", which is a quote form The Restaurant at the End of the Universe by Douglas Adams.

As for the feelings it invokes, the words would be very different - "unease" for example.

Solution 3:

contrived

having an unnatural or false appearance or quality : ARTIFICIAL, LABORED m-w

Deliberately created rather than arising naturally or spontaneously.

Created or arranged in a way that seems artificial and unrealistic. Lexico

If you see something that seems fake since it was too perfectly planned out, call it contrived. Vocabulary.com

But the modern practice of urban development does not have these features. It does not deal with growing wholes at all.

First, ...

Second, the growth is not, in any deep sense, unpredictable. It tends, most often, to be controlled by conceptions, plans, maps and schemes. But these plans do have the capacity to generate a growing wholeness. Instead the force an artificial, contrived kind of wholeness.

Third, ... The order is superficial, skin deep, only in the plan or in some contrived orderliness of the arrangements. There is no deep inner coherence, which can be felt in every doorway, every step, and every street. ref.

Boston itself was a more peaceful city than New York, and had a charm reminiscent of a European town, with its less-planned, less-contrived layout reminding him particular of Rouen, and its many gray and white buildings bring back memories of Paris. ref.

...a sort of Sundy-go-to-meetin kind of look about this part of the city, that I don't like a bit better than I do the pinched up, narrow contrived appearance of the rest. ref.

These geometric pools are often found in city courtyards or adjacent to period homes built in the French renaissance or Italian ... It is easy to make mistakes and end up with a contrived appearance when combining rocks, plants, and water. ref.

Solution 4:

it just feels as though the surface-level extravagance is hiding something.

façade noun (FALSE APPEARANCE)
a false appearance that makes someone or something seem more pleasant or better than they really are

Tacky (adjective)
Things that are tacky are cheap, flashy, garish, gaudy, loud, tawdry, or trashy. Tacky clothes are usually inexpensive yet flashy and showy — obnoxious.

Like the brilliance is only skin deep.

As others have mentioned, gold-plated, gilded. Sometimes written as gilt.

Like pretty wallpaper covering a rotting wall.

Paper-over (verb)
To hide an unpleasant situation, especially a problem or disagreement, in order to make people believe that it does not exist or is not serious

Solution 5:

Lexico gives:

Potemkin

Pronunciation /pəˈtem(p)kən/ /pəˈtɛm(p)kən/

ADJECTIVE (informal):

Having a false or deceptive appearance, especially one presented for the purpose of propaganda.

Origin: 1930s from Grigori Aleksandrovich Potyomkin (often transliterated Potemkin), a favorite of Empress Catherine II of Russia, who reputedly gave the order for sham villages to be built for the empress's tour of the Crimea in 1787.