Is there any mistakes in the following sentences?
1. New York has many famous art museums.
2. The city library is very busy on weekends. It has many interesting books.

Should I say “there are many famous art museums in New York”?

And , can we say “the library is busy”? I know I can say “library is crowded “

See a translation

@lester Both sentences are natural sounding.

1. "New York has many famous art museums." This a fine option for your already excellent sentence. Either sentence sounds quite natural.

2. "The city library is very busy on weekends...." I would not say "the library is crowded." Although, it is not inaccurate, when you use the term "crowded" is sounds like you're talking about a city bus or a restaurant during lunchtime. However, if the library is really that busy, I guess that sentence would work. My advice: stay with your original sentence.

PS: I just noticed a glaring error: Your question should read, "Are there any mistakes... " "mistakes" --> the plural here requires the plural verb form.