A great plot could involve the two heroes swapping cities for a while. Arrow tries to deal with Gotham's crime underworld while Batman goes to Starling City to investigate a series of strange disappearances that might be linked to a powerful criminal organization there. This would lead to both heroes having to adapt to different environments and crime - fighting styles.
One idea could be that Batman and Arrow team up to take on a common enemy like Ra's al Ghul. Since both of them have had run - ins with him in their respective storylines, it would be cool to see them combine their skills and resources to fight against him. Another plot could involve a mystery that spans both Gotham and Star City. Maybe there's a new criminal organization that's using technology from both cities to carry out their evil plans, and Batman and Arrow have to figure out how to stop them while also dealing with the differences in their methods of crime - fighting.
One idea could be Batman coming to Star City to help Arrow deal with a new, extremely dangerous criminal organization that has ties to Gotham. This could lead to some great fight scenes as they combine their skills and resources.
One idea could be that Arrow is transported to Gotham and teams up with Batman to take on a common enemy like Ra's al Ghul. They could combine their skills, with Arrow's archery and Batman's detective and combat skills.
One idea could be that the Flash and Arrow team up to stop a meta - human who has the ability to control time. They have to race against the clock (literally) to figure out how to neutralize the villain's powers before he rewrites history in a way that destroys Central City and Starling City.
Well, a great plot for Supergirl Arrow crossover fanfiction could be centered around a common enemy from another dimension. This enemy has technology that nullifies Supergirl's powers and Arrow's skills, so they have to rely on their wits and each other's unique strengths. For example, Supergirl could use her heat vision in a creative way to expose the enemy's weaknesses while Arrow uses his archery skills to set up distractions. They could also meet some interesting characters from the other dimension during their adventure.
One idea could be that an alien threat emerges which requires the skills of both Arrow's team in Star City and Supergirl in National City. They have to combine their combat styles, with Arrow's more grounded and stealthy approach and Supergirl's super - powered attacks. For example, Arrow could use his trick arrows to create distractions while Supergirl takes on the stronger alien foes directly.
One idea could be that the characters from Torchwood and Arrow team up to fight a common enemy that has some sort of interdimensional powers. Maybe a villain from Arrow's world has found a way to access Torchwood's technology and is using it for evil, and the two groups have to combine their skills to stop it.
One idea could be that a powerful villain threatens both Star City and National City simultaneously. Arrow and his team are struggling with the more street - level threats in Star City, while Supergirl is dealing with the super - powered aspects in National City. Eventually, they cross paths when the villain's plan connects the two cities. For example, the villain might be using some sort of technology that is affecting the meta - humans in National City and also causing chaos in Star City's criminal underworld.
Maybe there's a meta - human or a super - villain who is causing chaos in both cities. Batman is too occupied with Gotham's internal affairs, so Arrow comes to help. They discover that the villain has a base in an abandoned area between the two cities. They have to combine their resources, like Arrow's high - tech arrows and Batman's detective skills (even if Batman himself isn't directly involved but his influence on Gotham's crime - fighting is there), to take down the bad guy.
Perhaps there could be a story where Lex Luthor somehow gets hold of some of Arrow's technology and Clark has to work with Oliver to retrieve it. They would have to combine their skills, Clark's superpowers and Oliver's archery and combat expertise.