The closest jet airport is Sunshine Coast Airport at Maroochydoore (30 minutes drive south). There are direct flights from Brisbane, Sydney and Melbourne. The trip from Sydney takes around 1 hour 25 minutes, from Melbourne takes around 2 hours 25 minutes & the flight from Brisbane takes about 30 minutes.
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If you are travelling by car the following times will give you an idea of how long the trip will take, factoring in a couple of short stops.
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There are a number of coach services that pass through Cooroy on the Bruce Highway (about 15 minutes drive away) and there are connecting busses to Noosa. Some services go into Noosa itself and there are local services operating between Cooroy, Tewantin, Maroochydore (Sunshine Coast Airport) and Noosa. The bus trip from Brisbane takes around 2½ - 3 hours.
The closest train station to Noosa is at Cooroy, around 15 minutes drive west from Noosa. There are more frequent train services to Nambour which is about a 30 minute drive south from Noosa. Regular bus services operate between both train stations and Noosa.