Indonesia has about 50 airports and there are several reliable airlines. The main airports (including Jakarta (Java), Surabaya (Java), Medan (Sumatra), Makassar (Sulawesi) and Denpasar (Bali) are modern and well-serviced (24/7) as you'd expect from a country where air travel is necessary and has a population ten times larger than Australia. There are direct flights to all the popular destinations including Labuan Bajo (Flores/Komodo), Sorong (Raja Ampat), Ambon (Maluku) and Yogyakarta (Java). Other destinations are usually no more than a brief stop. From the main regional hubs, you can get to anywhere within a short flight (usually either direct or 1 stop).
Garuda Indonesia, the country's principal airline, won world's best cabin crew in 2017 and 2018, ranks highly in airline safety ratings and has surprisingly comfortable, spatious seating (boasting some of the best economy legroom in the region) and generous baggage allowance.
Most visitors from Australia would be used to flying into Denpasar to visit Bali but Garuda return airfares to domestic locations are easily competitive and avoid any complications with transfers and rescheduling - which is sadly commonplace these days among all major airlines.