English Translation
Please refrain from smoking in public places.
公共の場での喫煙はお控え下さい。
sounds more natural than 控えてください although 控えてください isn’t bad.
Inserting の makes the whole sentence meaning “you are okay to smoke somewhere else, but not here”. So, the speaker narrows down the prohibited area for smoking by inserting の.
お控え下さい is a common phrase for a notification or poster in a public space. It may look polite because of ください, but actually 控えてください isn’t polite enough in this situation.