Have been to Genoa once before, but really want to see it this time.
http://www.10cose.it/genova/cosa-vedere-genova.html
The website above is in Italian only, but it gives the list of things to do. And I agree those are the most important things to do in Genoa.
If you are from America you might want to add Columbus' house to the list. However it is not the original house which was destroyed by the French in the XVII century and then rebuilt. It's a museum about Columbus now.
Roberto's list is great. If you have time I would add the Mercato Orientale which is a huge indoor vegetable market off the Via XX Settembre. Also, eat as much pesto and focaccia as you can in your one day there!
Thanks, both.
Thanks for input. Have good ideas to work with!