Straight from Yahoo! Answers:
Answer 1: Classy refers to someone who has class as in a higher social standing. "Broad" is vulgar and is not a pleasant word to refer to a lady. It is a slang, offensive term and may refer to a promiscuous woman.
The label is used by lower class people to refer to a woman who has class except that they use the term "broad" because they are low-class themselves.
It is also old-fashioned and not in common used today. As the other answer stated, you will hear it used in older movies.
Answer 2: No, I'd say the opposite. It's how a working class character would describe a woman of standing. Depending on context, it can be used sincerely or mockingly.
It can be used to mean '****' when it is used sarcastically. "Yeah, she's a REEAALL classy broad... "