Early this year, I went to Lombok in Nusa Tenggara Barat with my travel buddies. It was my first time visiting Lombok (the world known tourist destination in Indonesia after Bali). These days, Lombok is getting more tourist attention especially after the opening of its new international airport. Airasia, for example, has just launched a direct flight from Kuala Lumpur to Lombok. I predict in the future, Lombok will gain more visitors as the local government has step by step started to promote Lombok as a tourist destination.
Different from Bali, the majority of the people who live in Lombok are Muslims. Still, there is a significant percentage of Hindu people in Lombok.
Hence almost similar with Bali, the major tourist attraction is the beach itself and the culture exhibition. Sasak people (the local ethnic of Lombok) usually live in the hut where they do handcraft and then sell it the tourist who drop by in their village.
The three main Gili (Sasak word means island): Gili Air, Gili Trawangan and Gili Meno is the main tourist destinations in Lombok. In my opinion, the islands are very similar with Kuta in Bali especially the Trawangan one. So many foreigner. I feel like I am not even in my own country when I was in Gilis.
The unique thing in Gili is there is no fuel transportation. You can only use cart with horse and bicycle to go around. While Senggigi, the beach in the main island, has lost its popularity these days probably due to the tourist expansion to the Gilis.
Like usual, the main activities that you can do while on island holiday are snorkeling, diving or other water sports (you mention!).