In English the verb to travel is the same as the Italian viaggiare, while the word viaggio has more than one translation: a journey is an act of travelling from one place to another, especially to a place that is far away; a voyage is a long journey on a boat or ship; a trip is a visit to a place that involves a journey, for pleasure or particular purposes; a tour is a journey for pleasure, during which you visit several different places; travel is the general activity of moving from place to place: air travel, road travel, business travel, space travel.
to go/be on holiday: Every summer we go on holiday to Spain.
to take a trip: I'm thinking of taking a trip to the seaside for Easter.
to go on a trip: He's going on a business trip to Japan next week.
to make a journey: In search of food, they made a journey to a more fertile country.
to be en route: Is there a flight en route from Tokyo to Sydney?
to cross: They had just started to cross the desert.
to be on the move: The circus is on the move again.
to tour: The theater company is touring Italy.
to have a safe journey: They rang to wish me a safe journey.
a traveler/traveler: someone who travels a lot, either for work or pleasure.
a passenger: someone who is travelling in a vehicle, boat, or plane, but is not the driver.
a commuter: someone who lives in a different town, city, from the one where they work, and who therefore travels a long distance every day to get to work.
a globetrotter: someone who travels around the world a lot, especially for their work.
a holidaymaker/a vacationer: someone who is spending time in another place or country for enjoyment.
a tourist: someone who visits a different place for interest and enjoyment.
a hitchhiker: someone who travels by standing at the side of the road, asking people in cars to stop and take them to the place they want to go, often without payment.