Hush could be an interesting choice. He could be spreading false rumors and causing distrust between the heroes and the citizens of both cities. His knowledge of Gotham's underworld and his ability to manipulate people could make him a formidable foe for Batwoman and Arrow. They would need to uncover his true identity and stop him before he completely destroys the relationship between the two cities.
A cool concept could be a crossover where the technology in Gotham and the magic in Star City somehow get mixed up. Batwoman, being more used to high - tech gadgets, and Arrow, who has some experience with magic - related threats, have to combine their skills to set things right. For example, a device that was supposed to enhance Batwoman's suit ends up being enchanted by magic from Star City, and they need to figure out how to fix it and stop the villain who caused the mix - up.
Batwoman is portrayed as gay in comics. Her sexuality is an integral part of her character and has been explored in various comic issues and storylines.