Sunnygirl
Please Please Please do NOT go AI. There are so many restaurants as Clarets4ever has said. You will be spoilt for choice and you can make your meal as cheap or as expensive as you like. The local bars and restaurants are being killed off because of these AI hotels, and do you really want to be sitting with the same people every day/evening whilst your eating, and be told what time you are going to eat. I would also go with claret on booking a private apartment. With three kids you want bit more room than a hotel can offer and you are not guided by their meal times etc. With kids of 16,14 and 7 I would be out all day be it an excursion, the beach or simply around the pool, and if they are enjoying themselves they are not going to be happy being told they have to go back to hotel for dinner. You will have so much more time and freedom to enjoy the island if you stay in an apartment. I bet if you book a private 2 bed apartment include your food, spending money and flights it will work out cheaper than booking a hotel, especially in school holidays. The areas I would consider are Costa Adeje, Fanabe, and Los Cristianos
Can you tell I love Tenerife [that's why I moved here]