If you think that hiking Mount Rinjani is not your thing, you can consider hiking Bukit Pergasingan instead. Several great things can be found from this hill which is located in Sembalun, not far from the starting point of Mount Rinjani hike.
Gili Air might attract many tourists to spend time but you should consider visiting Gili Kedis if you really want to get away from tourism crowd. Gili Kedis has some good things which can give you unique experience after all.
Your friend, who has been in Lombok, may put the island on the list of recommendation. S/he will tell you that Gili Air has wonderful beaches and it has long become an island where you could dive and doing other things like snorkeling