Being a major city of Australia, Sydney is very well connected globally, and locally. It can be reached via it's international airport, with all the major Australian cities by bus and also via train and is easily accessible via car as well.
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How to Reach Sydney from India
Flights connect Sydney to all major airports in India, though there are no direct flights from any of these. Most of the flights from the smaller international airports first go to Delhi, from where they're changed first and then there is usually another stop over in the Singapore-Malaysia-Bangkok area. Air Asia, Jet Airways, Thai AIrways, China Southern, Singapore Airlines and Cathay Pacific are some airlines providing services on this route.
How to reach Sydney by flight
Sydney's international airport, the Sydney Kingsford Smith International Airport, is the busiest airport in all of Australia. It's extensively connected to almost all countries of the world.
Domestically, Sydney airport can be reached from other regional capital airports only.
How to reach Sydney by road
Sydney is easily reachable via car. Australian highways are quite scenic and you can drive down from Melbourne and Brisbane both in under 12 hours. Adelaide is little further off and a 2 day direct trip would be needed.
How to reach Sydney by train
The rail networks connecting Sydney to the rest of Australia are fairly decent. The New South Wales Trainlink connects Sydney to all the capitals and nearby towns and cities of NSW. The Indian Pacific rail network connects Sydney with Perth.¾
How to reach Sydney by bus
Like rail, bus routes are connected to Sydney from all the capitals and also from the entire NSW region. However, buses are usually preferred over trains, and they're very easy to book as well.
How to reach Sydney by Waterways
Sydney's harbour is one of the busiest. Circular Quay, the main Sydney harbour is the place where most of the international cruise liners dock. Many of these are coming from the Pacific region and the Asian region.
Local transport in Sydney
Sydney today has decently connected bus and rail services throughout the city. The train services are operated by the Transport for New South Wales, while the bus services are managed by the government and private contractors both, the former controlling the areas previously accessed by trams, and most of the others operated by the latter. Even the ferry system of Sydney is quite well adapted, with it's main terminal at Circular Quay. The Opal Travel pass makes it very easy to travel in the city. You can top it up with money and then use it on the go across all modes of transport.