The quickest way to access Katherine is to fly in to Darwin, hire a car and drive south down the Stuart Highway.
By plane
Just south of Katherine is the Tindal Airforce Base. This is also the airport for Katherine, however no schedueled domestic flights fly to or from here. You may charter an aircraft into Katherine.
Darwin International Airport (http://www.ntapl.com.au/D...) is the closest schedueled flight airport to Katherine.
Airborne Solutions (http://www.airbornesoluti...) phone - +61 8 8972 2345, fax - +61 8 8972 2535 prices range from $920-2320
By train
The Ghan (http://www.gsr.com.au/our...) train travels north twice weekly to Darwin from Adelaide via Katherine, and is one of Australia's most spectacular rail trips. The train stops for a few hours in Katherine, and there are a selection of off train tours that you can do. These are organised on the train when it is arriving into Katherine.
By bus
Greyhound bus services Katherine. Their office is located at BP Travel North on Katherine Terrace.
By car
Katherine is around 3 hours drive and around 300 km south of Darwin. All cars rented direct from the rental companies in Darwin will have per day kilometre restrictions. Unlimited kilometres rentals are unheard of in Darwin unless hiring a campervan.
Unlimited kilometre car hire rentals can be obtained by booking through travel wholesalers such as Territory Discoveries and Flight Centre which makes car hire much more affordable. Be careful though, if you are just booking through a consolidator, rather than a wholesaler, the kilometre restrictions will definitely apply.