Having lived six years in Genoa and having had a very good time there I still have a special link with this town. But also without sentimental links to visit Genoa it is really worth the trip as it has medieval monuments, navigation history, wonderful food and perfect beaches nearby. You will not regret it.
The problem about the town is that it is very complicated to drive and nearly impossible to park so you need a location in the center allowing you to walk nearly everywhere or to get the public transport easily.
And here it is. If you would like to rent a very nice and completely refurbished apartment in the heart of town, this one belongs to a dear friend of mine, Betta, who restored it from scratch a few years ago, lived there for a while and now moved to another apartment out of town.
It is perfect for two people and it has an open space with living room and open kitchen fully equipped, big wardrobe room and one bedroom overlooking the living area. Bathroom and laundry room. Rates are around 100 Euro per night depending on the season and you can book via airbnb.
I really recommend it and I grant you you will be in the best part of town.