Midori no Hibi, Clannad Recommendations
The lead character from "Clannad" and "Midori Days" is viewed as a delinquent amongst his schoolmates. However, due to his heart of gold and the kind things he does to help others, multiple girls fall for him.
The female protagonist of both series can be described as naïve and shy with similar personalities in general. She is someone who is able to bring out the best from the delinquent she fell in love with as they go through hurdles in life and school together.
Furthermore, there are fights or beat-downs against rowdy gang members who initiate violence.