The volcanic nature of the islands leads to some incredible underwater formations, discoverable only by donning scuba diving gear and taking a dip in the crystalline waters. There are dozens of dive sites to explore, each with its own compilation of excellent diversity.
Many scattered islands are ripe for scuba diving off the northern shore of Java, archipelagos of tiny isles. Karimunjawa is an especially nice archipelago, with lovely, protected corals and several shipwrecks.
Once you fly in, public transportation is your best friend. Get around towns by taxi or bicycle. Getting from town to town is best accomplished by bus or train.