Sounds good! You need a comma after "read". You might consider using the infinitive "to talk", but often the "to" is dropped in conversation. Example: "The library is a place to read, not to talk."

depends, are you saying it or writing it? It is understood well for speaking. I believe a more grammatically correct way is "The library is a place to read--not to talk". Another way: "The library is a place for reading--not for talking".