They could face a villain who has the power to control technology. This villain could use their powers to disrupt the city's infrastructure, and the main character with Spiderman powers would have to use their agility to stop them from causing more chaos.
A mad scientist could also be an enemy. This scientist might be jealous of the main character's powers and try to create his own version of the powers but with a more evil intention. The main character would then have to use their wits and powers to stop the scientist from creating a dangerous army or something equally bad.