Learn Hardcore Polish: Wyjście z parkingu jest naprzeciwko ratusza, przy dużym skrzyżowaniu. - The exit from the parking lot is opposite the town hall, by the big intersection.

Because the preposition z (meaning from/out of) takes the genitive case. The noun parking is masculine and its genitive singular is parkingu, not parkinga. Many inanimate masculine nouns ending in a hard consonant take genitive -u.

Nominative: parking
Genitive: parkingu
Locative: parkingu
Instrumental: parkingiem

Why does naprzeciwko take ratusza? What case is that?

Naprzeciwko requires the genitive. Ratusz (town hall) is masculine; its genitive singular is ratusza. So naprzeciwko ratusza = opposite the town hall.

Nominative: ratusz
Genitive: ratusza
Locative: ratuszu

What case does przy take? Why is it przy dużym skrzyżowaniu?

Przy takes the locative case. Skrzyżowanie is a neuter noun; its locative singular is skrzyżowaniu. The adjective must agree in case, number, and gender, so duży becomes locative neuter dużym: przy dużym skrzyżowaniu.

What is the difference between wyjście and wyjazd? Which fits best here?

Wyjście = exit for pedestrians (the act/place of going out on foot).
Wyjazd = exit for vehicles (the act/place of driving out). With parking (a car park), if you mean where cars leave, say Wyjazd z parkingu. If you mean the pedestrian gate/door, Wyjście z parkingu is perfect.

Can I write na przeciwko instead of naprzeciwko?

No. The correct, standard form is the single word naprzeciwko. You may also use naprzeciw (one word), which is a bit more formal/literary: naprzeciw ratusza.

Is naprzeciw interchangeable with naprzeciwko?

Generally yes; both take the genitive and both mean opposite. Naprzeciw can feel a touch more formal. Avoid przeciwko here; przeciwko on its own usually means against (e.g., przeciwko planowi = against the plan), not opposite.

Is the comma before przy dużym skrzyżowaniu necessary?

It’s optional style. You can separate two parallel adverbial modifiers with a comma to improve readability: …jest naprzeciwko ratusza, przy dużym skrzyżowaniu. Without the comma is also acceptable.

Can I change the word order?

Yes, Polish word order is flexible. For example:

Wyjście z parkingu jest przy dużym skrzyżowaniu, naprzeciwko ratusza.
Przy dużym skrzyżowaniu, naprzeciwko ratusza, jest wyjście z parkingu. Just keep z parkingu directly after wyjście because it belongs to that noun phrase.

How do I pronounce the tricky parts?

Approximate IPA (main stress is always on the penultimate syllable):

Wyjście [ˈvɨjɕt͡ɕɛ]
z parkingu [s parˈkiŋɡu] (the z often devoices to [s] before [p])
jest [jɛst]
naprzeciwko [naˈpʂɛt͡ɕifkɔ]
ratusza [raˈtuʂa]
przy [pʂɨ]
dużym [ˈduʐɨm]
skrzyżowaniu [skʂɨʐɔˈvaɲu]

Why is it dużym and not duże or dużego?

Agreement with case and gender:

Nominative neuter would be duże skrzyżowanie (a big intersection).
After przy (locative), the forms are dużym skrzyżowaniu. So dużym matches neuter locative singular.

Why not use od to say from, as in od parkingu?

Od means from in the sense of source, origin, or distance away from (e.g., kilka metrów od domu = a few meters from the house). To express movement out of an enclosed/area space, Polish uses z: z parkingu = out of the parking lot.

What is the difference between ratusz and urząd miasta?

Ratusz is the town hall building, often historic, on a main square.
Urząd Miasta is the city office/administration. In some cities they’re in the same building; in others they’re separate.

When do I use ze instead of z? Why is it z parkingu, not ze parkingu?

Use ze before certain consonant clusters or words starting with s-, z-, ż-, rz-, ś-, ź- to ease pronunciation: ze szkoły, ze mną, ze Zbyszkiem. Parking starts with a simple p, so plain z is natural: z parkingu.

Could I say znajduje się instead of jest?

Yes. Znajduje się sounds a bit more formal/neutral and is common in signage or written directions:

Wyjście z parkingu znajduje się naprzeciwko ratusza, przy dużym skrzyżowaniu. Using jest is shorter and perfectly correct in everyday speech.

Does Polish need a word for the before wyjście?

No. Polish has no articles. Wyjście z parkingu can mean the exit from the parking lot; definiteness is inferred from context. If you need to be very specific, you can add context or a demonstrative, e.g., to wyjście (this/the exit).