The are around Ubud is really nice, but where-ever you go around there you will get Monkey visitors, and the ones that wander the furthest from the monkey forest tend to be more aggressive in their nature.
I'd advise avoiding the south of Bali - particulary Kuta, and looking towards the northern parts of the island. Your best bet to find a good location for a romantic get away is to ask on a forum like the thorn tree
http://thorntree.lonelyplanet.com/ca...s.cfm?catid=23 - though this is primarily for travellers, my experience is that a lot of the people who actually answer questions either live there or have done in the past...
If you want to see the island, my suggestion would be to befriend a local and offer them a reasonable amount (a few hundred HK$) to get them to show you the island. This way you can get to see the parts that arent covered in backpackers and you may even get to see their home village. However, you should be wary that their are a lot of people who will offer to show you about will take you an art gallery where you will be badgered into buying something, or to an impoverished village where they will try and get money out of you...
However, it is a beautiful and relaxing island, good luck
