Travelling around Indonesia requires the use of the national airline Garuda, although smaller companies operate charter flights on some routes. The roads in the country are good, and hiring a car is an option, although it is a better idea to pick up a local driver for their knowledge rather than going it alone.
Ferries are the best way of getting around the smaller islands like Lombok, and tickets are normally best bought at the jetty before setting off.
Within Jakarta, taxis are the most sensible way of getting around the city, and take the headache out of trying to find you own way from one place to another.