If you’re looking for quiet places to stay in Kuta I’ve got two recommendations. The first is a quiet as a morgue and the rooms (especially those at the back) had a feeling of privacy to them. It is Berlian Inn and costs 60,000 per night for basic budget accommodation with a few nice touches – outdoor bathroom, shower, wardrobes, matching linen on beds. It's located just off Poppies Lane 1 (is in the Lonely Planet guide).
The other place was the best value accommodation I stayed at on Bali – Kedin’s 11, which is in Gang Sorga, also off Poppies Lane 1. The rooms are large, beds have good mattresses, matching linen and there’s a wardrobe, clean bathroom and effective ceiling fan. There’s also a decent sized pool and nice lounging area – all for 70,000 a night. Bargain!