Good question Ronny! Indonesia is a huge country with many islands that are yet to be explored.
The most popular of the islands is Bali with a thriving night life and developed tourism sector around the kuta beach area. Around Bali you can find many things to do. Down south in Uluwatu you find amazing surf spots and stunning views from the cliffs around Padang Padang. In the center of Bali in a town called Ubud you can find all sorts of craftmenships and art created by the locals. like paintings, wood work and stone crafts. In Ubud you can also find the Monkey Forest This place is runned by monkey’s so don’t bring to many valuble belongings with you! You can also find a vulcano up north.
Lombok is also a beautiful island that is located a 4-6 hours (depending on waves) ferry ride east of Bali. The big difference of the two is that Lombok is more quiet and under developed than it’s big brother. The people are Muslim while Balinese people are Hindu’s. In Lombok you can find amazing surf down south, in kuta Lombok and gerupuk. In Gerupuk the fishermen will take you out to the wawes by boat for around 100.000 IDR and I promise you that the waves won’t disepoint you. Lombok also has an amazing and unique mountain with a lake on top of it called Lake Segara, in the middle of that lake you will find and active volcano that is currently forming a second mountain. On the north west tip of Lombok you will also find the thee infemous Gili Islands, trwang, meno and air. They are also worth a visit if you like to snorkel or scuba dive with turtles and other fish.
There is so much to explore in this huge country with it’s 17,000 islands. My tip to you and your girlfriend would be to start with Bali or Lombok. Is it to crowded? Start island hopping to you find the right place that fits you.