My wife and I spent three nights at The Puncak (which, not surprisingly, means 'The Summit' in Bahasa). It is indeed located near the top of a steep hill overlooking the water—some taxi drivers seemed to need a little coaxing to take their vehicles all the way.
The owners Jean-Paul and Nury built The Puncak as a labor of love, and just imagining all the work they put in is staggering. We ended up being the only guests during our stay, so the quiet location was made even more quiet. Upon arrival our bed frame was covered in dozens of fresh flowers from outside, and each morning we were served a sumptuous breakfast of eggs, yogurt, fruits, and more outside our room. The room itself was very spacious—but unfortunately that meant the AC unit struggled to cool the air, making the nights fairly warm.
Location-wise you're about an hour from the airport, 10min from the restaurants of Senggigi, and 30min from Bangsal, where you can catch boats to the Gilis. Aside from relaxing in the infinity pool, there's not much to do here on the grounds.
If you're looking for an affordable, secluded base for Lombok lounging, this is it!