Genoa is a great city in which to spend a few days, mostly because you can take your sightseeing relatively slowly and still have time for a top-notch day trip.
You can walk 1.5 miles on the Corso Italia all the way to the little fishing village of Boccadasse, which gives you a chance to see what a small Genoa neighbourhood looked like before it was a big city and also to take advantage of nice weather.
There are several museums worth checking out on the fashionable Via Garibaldi in Genoa's historic center. These museums and galleries were once private palaces – the entire street is lined with buildings that used to be the homes of Genoa's wealthy families – and they give you a fantastic look not only at some beautiful artwork but also how noble families lived in the 17th and 18th centuries.
For those of you who'd like to get out of the city, you could go to the picturesque town of Portofino for high-end shopping and leisurely dining.