Rapallo's position in the middle of the Tigullio Gulf makes it an excellent base. Portofino is the obvious first choice — 15 minutes by ferry in summer, a little longer by road. The village is small and the harbour is one of the most photographed in Italy; go early in the morning or late in the afternoon to beat the day-tripper crowd.
The Cinque Terre is reachable by train (change at La Spezia) or by summer ferry, which calls at the villages from the sea. Riomaggiore is the closest village; the full ferry run covers all five. Chiavari, the next major town east along the gulf, is 20 minutes by train and has a good antiques market on the second weekend of each month.