Genoa has an international airport (GOA) with flights from London Gatwick and Stanstead, as well as Paris, Rome, Zurich etc. Genoa Airport has a cheap Airbus link to the main station (Genova Piazza Principe). Note that tickets for rail and buses have to be bought before boarding. Stamp your ticket before boarding a train if you don’t want to pay a heavy fine. When boarding a bus, stamp your ticket as soon as you get on the bus. Naturally, you should always keep careful watch over your belongings.
Nice (France) also has an international airport, connected by bus several times a day to Genoa.
Pisa (about 2 HRS by rail from Rapallo) has good and cheap international flights.
Make sure you validate your tickets by stamping them before boarding your train. Cheaper fares are sometimes available on IC and Eurostar trains if you make your reservation beforehand on line.
There is nothing short of mayhem in Rapallo on 3 July (“Festa della Madonna di Montallegro”), so if you come by car make sure you arrive no later than 4 PM. The city will be completely jammed from 8 PM until after midnight. A traditional religious procession makes its way through the town from about 7PM, starting from the main church. The floating lights are usually displayed at about 9 PM. Fireworks start at about 10 PM at the old Castle on the waterfront.