"Museums are important cultural buildings."

Translation: A múzeumok fontos kulturális épületek.

[gr8fuld34d]

Why are "fontos" and "kulturalis" in singular form when they come after a plural noun?

[vvsey]

They are not after a plural noun. They are in front of a noun: "épületek". They do not belong to the subject, they are related to (or part of) the predicate.
And adjectives before nouns stay singular.

[BaloghTams19]

I would rather say "institutions" (intézmények) instead of "buildings".