One of the best things you can do in Portofino is relax. Walk around the small city, hear the sea, take a rest at the end of the left Marconi quay. There is a small wine bar where you have an occasion to drink something seated less than one meter from the sea.
Usually all the boutiques are open from the end of February until the end of October. Don't forget to bring something for your shoulders even if you came in the summer time. After 6/6.30pm the sun goes behind the Portofino promontory and cools off considerably.
Also, you can visit San Fruttuoso Bay and try to see the sculpture of Christ of the Abyss. You can reach San Fruttuso only by sea. You can choose a public boat at reasonable price. If the money is not a problem, try to rent a small taxi boat. It's an unforgettable experience.
If you have some days off, you can also visit the Acquarium on Genoa 30 km from Portofino - the biggest one in Europe - and walk around the port streets. There are a lot of museum and historical buildings.
