Perhaps the main plot is that Kobayashi San's loved one is kidnapped in River City and a ransom is demanded. Kobayashi San has to stay calm while trying to gather the ransom money and figure out a way to rescue the hostage without getting caught by the kidnappers.
The title 'Stay Cool Kobayashi San A River City Ransom Story' gives the impression of a story full of suspense. It could be that Kobayashi San is an ordinary person thrust into an extraordinary situation in River City. The ransom aspect implies that there is some sort of threat or blackmail involved. Maybe Kobayashi San has to use their wits and courage to resolve the situation while staying calm. It might also explore the culture and environment of River City as part of the backdrop to this intense situation.
The 'River City Ransom' story is about a game where players are in a city full of thugs. You play as a character who has to fight through the city to rescue someone or achieve a certain goal. There are different levels and enemies to face. It has a unique retro style that many gamers like.
I'm not entirely sure as I haven't played this specific 'River City Ransom Underground Story' in great detail. But generally, it might involve the typical elements of the River City Ransom series like street battles, rescuing someone, and exploring an underground area filled with various enemies and challenges.
The story of River City Girls 2 likely involves the girls from the first game getting into new adventures, facing tougher enemies, and exploring more of the River City world. Maybe they are on a quest to save the city once again from some new evil force.