I've stayed in Bali a couple of times. If you want the exciting crazy life with other tourists, then you can go to Kuta... unfortunately, the sea is absolutely filthy on that side. Just sit on the beach and watch the sunset. However, I was recommended a hotel (Hotel Sorga) which was tucked away in the centre, so it was peaceful once I was inside.
The first time, I stayed on the opposite coast in Sanur (I think in Gazebo Beach Hotel... it was OK). It was much more peaceful and the beach was clean. You'll need to take an ojek if you want to visit the touristy places in Kuta and Legian, but if you generally want peace and quiet I recommend Sanur.
Of course, there are other places (Ubud, Denpasar, etc) you can visit if you prefer somewhere inland.