River City Ransom, released by Technos Japan in 1989, is an action game with RPG elements (yes, you can strengthen and customize your player). I remembered putting in a lot of play time with this game. Very cool game!
Object of the game: Guide the high school students Alex or Ryan (or both as a 2-player co-op) through their city while fighting off gang members and their boss leaders in order to rescue Ryan’s girlfriend, Cyndi. You collect money from defeated gang members in order to purchase food, medicine to boost your base stats. The coolest part is you can purchase Techniques which improves your character’s fighting moves. Dragon Feet, anyone???