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Ibiza is such a small island that even though you can get "off the beaten path" you really won't have to go far to do so. The best way to stay somewhere a little unique is to try out one of the eco-hotels or rent a villa. There are superb hotels such as Atzaro, Can Gall, Palerms de Jardin, les Terrasses and Can Curreu. They are all set in the countryside, extremely private and so very laid back. You can see some on www.mrandmrssmith.com. Another really good way to keep your privacy is to rent a villa. For a group of people they aren't as expensive as they seem and can be cheaper than staying in a hotel. The local experts are www.ibizatravelshop.com.
You'll need to hire a car to get out of the main resorts and start to drive around. To really get away from things tour the north of the island - head for san carles, can joan, cala llenya and cala mastella. For a great little beach try S'Estanyol on the way to the very end of Talamanca - it's quite a drive down to but worth it when you get there.
It's hard to keep away from the crowds in Ibiza in the height of summer, but easy to find a small tapas place or bar in one of the many villages in the centre of the island - where tourists fear to tread and the place is untouched by modern life.