In a quiet lane near the Maddalena church, the easy-going Manêna was Genoa's first hostel to open in the historic centre back in 2012, and it's still one of the best. Dorms have five to 12 beds, with tall ceilings, decent natural light, and privacy curtains (and reading lights) in the bunks. There's also a kitchen.
The young, friendly staff is happy to share tips, and the free walking tours and pub crawls are good activities to meet other travellers.