Traveling with 3 children ages 14, 11 & 9 to Santorini in the summer. What part of Santorini should I stay in?
Good question, one that's been discussed ad infinitum. The "party line" is that there's not a lot for kids to do in one of the clifftop villages, that they have easy access to the beach if you stay on the other side of the island in Perissa Beach or Kamari Beach. This is true if the beach is your priority, as long as you understand that they're black sand/pebbles/rock and because they're black they get very hot on the feet. Along with that is the fact that in most places along the beaches the water drops off fairly quickly into deep water. I think the most notable exception to the deep water dropoff is the north end of Perissa Beach, but the underwater shelf is slippery with algae. No heavy waves, though, it's very calm. Even shallower is the beach at Monolithos Beach, which is near the airport, but there's not a lot to see or do there.
The Meltemi Resort in Perissa might be a good fit, and there's a small waterpark for kids nearby.
All that said, if a swimming pool is more your style you can stay wherever you like. There are lots of family-friendly hotels with pools all around the island, and in Oia there is a lovely public-access pool that's free if you buy food and/or drinks: http://www.lioyerma.gr This makes Oia a lot more affordable than some would have you believe and offers you the chance to stay in the most beautiful village on the island. Check the Anemomilos Hotel, Laokasti Villas, Aethrio Hotel and Olympic Villas for hotels with pools. There are many more and the room rates vary a LOT.
Fira, the main village and island's social/commercial center, is also a good option. The island's bus hub is there and there's plenty to see and do within easy walking distance to most hotels there. Some of the hotels back away from the cliff have very large pools. I don't know what your budget is but one with a good view and a fair price for what you get is Volcano View Hotel and Villas. Also have a look at Villa Ilias.
If you want a quieter option with a view of the caldera check in Imerovigli. For example, look at Caldera's Memories and Gizis Apartments.
In general, the best way to search for what you need at the price you can afford is to use the filter system at http://www.booking.com Be advised that many hotels are not yet booking for next summer and that system will kick out a message that a hotel is fully booked on your proposed travel dates when in fact it's not. You'll have to check back after the first of the year and keep checking until you see trial bookings being accepted. You will also find a few that do book this far in advance but most will not. What you can do is search for hotels village by village and read the reviews left. You can also read more reviews on www.tripadvisor.com, which is a very informative website.
This is the best map I know of for Santorini: http://www.santorini-web.com/map.pdf