If you are looking for a relaxing place with lots of privacy, you will really like Villa Kaba Kaba. We had two villas and a private pool, plus a private living room/kitchen/TV room. The staff was superb.
There are a couple of drawbacks. One is that they only take cash. The other is that it's a long drive to anywhere, including lunch and dinner spots. Count on 30-45 minutes each way. The villa provides a car and driver free for seven hours a day, but since you need to go somewhere to get those meals (unless you prepare them yourself in the kitchen), you will be paying overtime if you want to leave in the morning and come back after dinner. That's also the case if you leave in order to go to lunch, return, and then head out at dinner. On the flip side, if you want to head up north to the volcanos, or to other parts of the island, you save time by avoiding the terrible traffic in Kuta, Ubud and Denpasar.