You can reach Rome from most major international airports in India. However, most flights have a stopover, so plan your trip keeping that in mind. Qatar Airways, Turkish Airlines, Air India (which offers stopovers in India itself) and Etihad Airways are all good options.
Rome has two international airports - Leonardo da Vinci/Fiumicino International Airport and G.B. Pastine/Ciampino International Airport.
Rental cars are easily available from any one of the rental companies across Europe. However, it is advisable not to drive around the city itself, as traffic is chaotic and cars are a very slow mode of transportation. Rome is surrounded by the Grande Raccordo Annulare, a round ring of highways that basically surrounds the city.
Rome is well connected to the rest of the country by the railways. The main terminal is called Roma Termini. Alternatives to Roma Termini are Roma Tiburtina, Roma Ostiense, Roma Trastevere and Roma Tuscolana.
This isn't a very popular option, but if you do want to travel by bus, Eurolines bus company is pretty much your only option.
The closest port is Civitavecchia and this is where most cruise ships stop or start. To reach Rome, you can take the train from here, as Rome is about an hour and a half away.
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