From Genoa, most of the beatiful locations in Italy, South France, and Switzerland can be reached. Some examples (with different distances) are provided here.

Portofino – 40 min. train/bus, 45 min. car
Cinque Terre – 1 h 15 min. train, 1 h 30 min. car
Sestri Levante – 40 min. train, 30 min. car
Portovenere – 1 h 50 min. train/bus, 1 h 40 min. car
Alassio – 1 h train, 1 h 15 min. car
San Remo – 1 h 50 min. train, 1 h 45 min. car
Cannes – 3 h car, 4 h train
Nice – 2 h 30 min. car, 3 h 20 min. train
Cote d’Azur – 2 h 20 min. car, 2 h 30 min. train
Pisa – 1 h 50 min. train, 2 h car
Turin – 2 h train, 2 h car
Milan – 1 h 30 min. train, 1 h 40 min. car
Florence – 2 h 20 min. train, 3 h car
Venice – 4 h car, 4 h 20 min. train
Bologna – 2 h 30 min. train, 3 h car
Trento – 4 h car, 5 h train
Rome – 3 h 45 min. train, 5 h car
Naples – 5 h 30 min. train, 7 h car
Saint Moritz – 4 h 30 min. car, 6 h train
Courmayeur – 3 h car, 5 h train/bus
Lugano – 2 h 40 min. car, 3 h 15 min. train