If you arrives from the south are Bodø the place to stop.
From Bodø are there several ways to get out to Reine.
You can fly to Leknes airport. Wideroe is the name of the carrier.
From Leknes you can take the bus or rent a car.
The distance from Leknes til Reine er 55 km.
(ca 1 hour with the bus)
You may also take the ferry from Bodø to Moskenes. The boat ride is a fantastic trip. When you gets close to the island you se how the mountains rises up from the sea. A good way to see the midnight sun
The trip takes about 3.5 time. It arrives just 4 km fra reine.
Check time tables on http://www.torghattennord.no/