To travel between islands, you'll always have to fly with the Air Vanuatu. Prices for each flight are quite high. During high season, the shorter ones cost over €100 while the longer ones – for example Port Vila – Luganville cost over €200.
If, on the main islands – Efate and Espírito Santo – you insist on being totally independent, don't forget to rent vehicles with four-wheel drive. Leaving the city centers behind, the roads become deplorable. Expect to pay around €60 to €100 per day for a small jeep. A little less if you just rent an SUV. On the other islands, there is not even the possibility of renting a car or, if there is, it will be outside commercial rules.
Alternatively, in Port Vila (Efate) and Luganville (Espírito Santo) you can take a public minibus (1€ per way within the cities). At night, as the natives do, wave a cell phone or other light so that drivers know you want to get on board.
To visit places outside the cities, sign up for existing tours or charter a land taxi (55€ to 105€ per day) or sea taxi.