Hi Hamkin,
I think The Altinkum area is a great place to take children abroad for the first time. I first went to Altinkum with a friend 15 yrs ago, as she'd pinpointed it as the perfect spot to do classical sightseeing, and so it proved. Within an hour you have the spectacular hilltop Priene, a fabulously intact amphitheatre at Miletus, Herkalia at Lake Bafa - beautiful setting and great fish restaurants and at 1hr 45 minutes Epheses and St Johns Basilica at Selcuk (there is also an open air steam museum for young boys and a nearby beach for all). You can also take day trips to Bodrum by bus, coach or boat and daytrips to Kos and Samos by ferry.
On your doorstep is the Temple of Apollo at Didyma and a section of the Sacred Way (as walked by Alexander the Great) All of the above are great places for children to clamber and explore ancient ruins and the wildlife that lives on these sites (tortoises, insects galore etc.) There are also all day boat trips (good value) to local beaches, snorkling tuition, scuba diving, horse-riding, a local aquapark at Mavisehir and a very large one at Kusadasi, 1 hr 20 mins away.
All the beaches in the area are sandy and safe. They shelve very gently. They are very sheltered in Altinkum (choice of 3), which is why the main grew up there. It is an unpretentious beach resort, with Turks and British visiting in moreorless equal numbers. Increasing amounts of other nationalities too. Much international cuisine on the front. Some overpriced, but equally you can eat well at fast food restaurants with the same view. Behind the front are several kilometers of holiday houses before you hit Yenihisar where the locals live - an absolutely normal town, complete with cheap lokantas and a nice public park with play area and fountains (there are lots of playparks dotted around the area, with many restaurants having a playpark in their grounds). At Easter and Oct half term we use Altinkum's beaches (v. quiet then) otherwise we use local beaches at Mavihisar, which always have room. This is a more turkish area with a harbour with cheap cafes to watch the sunset from. It is about 20 mins from Altinkum, past the Temple but connected via very frequent cheap dolmus. Akbuk, in the other direction is also lovely - a low key, sleepy, spread out resort, with larger harbour area and more choce of cheap places to eat. Also connected to Altinkum by dolmus, but every 20 mins rather than every 5.
As accommodation in the area is very spread out. Hotels by the front suffer from noise at night (the turks come alive then!) It is worth considering complexes of apartments, whether privately owned or not. They tend to be a much higher standard than the hotels and many complexes offer courtesy bus services to the beach and town .Lots of restaurants, including the cheap lokanta in Yenihisar, offer a free door-to-door car service. The restaurant at the so-called 'third beach' near Didim Marina (with its Armani outlet store) offers a free car service if you take lunch there (good deal). If you go on an excursion, that will be door-to-door too. Car hire can be very reasonable (I paid £16 per day) but petrol is slightly more expensive than in the UK. Driving locally is pretty easy - local roads tend to be quiet.
Yenihisar has proper shops and large supermarkets, and open air markets abound. If your children do not take to Turkish food, or want some home comforts you can get many things from the UK from fruit shoots to weetabix minis. Likewise cuisine ranges from traditional turkish to sunday dinners!
Hope that gives a flavour of the place. We certainly enjoy going there with our two boys (now 8 & 3. Any other questions, do ask!