Camogli is about 45 km. west along the coast from the start of the Cinque Terre. It is on a promontory about 1 km. from Recco. There is a good rail link along the coast all the way from Genoa through Recco to La Spezia. You can check on train times on www.trenitalia.it (English language version) so if you have a good pool in Camogli you can always go out on the train for day trips to the Cinque Terre and save yourselves the hassle of moving with your baggage half way through your holiday.
My mom and I stayed at the Hotel del Cenobio too. It seemed a little overpriced to me but the hotel is right on the water and it was a great place to start our trip. Have the pine nut cake for dessert if you go there. Please see my other post about the Cinque Terre. You may pick up the train in Camogli - no driving required. Despite that since we were heading to Florence after, we drove to Monterosso, hiked to Vernazza, and then took the train back to our car. That is not a good hike for really little kids. It is strenuous even for adults in decent shape. I would suggest starting in Rio Maggiore. Be forewarned it is easy walking but really crowded.