What TMLAalum said. Cinque Terre is beautiful, but the cruise ships bring the tours there and it gets crowded on the trails. If you do Porto Venere, it's fun to explore and the higher you go , the better the views. The real town is on on Via Capellini. Must see sights include Church of San Pietro, the other big church - San Lorenzo, and Castello Doria, where a hike up the terrace will reward you with a panoramic view. To eat, try Portivene (Un Mare de Spori); Local dishes with a modern flair. They are closed on Mondays.
Crusing is a "gateway" to find something in which you are interested. Lots of good advice on this thread. If you do stay before and after your cruise, read a lot of guide books, consider hiring a local guide and buy your tickets in advance to the museums and sights, which are of interest to you.