Went there two days last October, here are the links for my blog... Well, it's written in French, but there are a few pics which might give you an idea of the place.
Day 1 in GenoaDay 2 in GenoaI recommend the aquarium, the marina, the old town, and try to get on that boat from the city's public transportation system, it's something like 2.20€ for an half hour boat trip in Genoa's port. Well worth it.