I also stayed in Scala when my daughter was 3, my current favourite at the moment is SKiathos though, suits just about everything your after, try http://skiathosinfo.com for some ideas about places

We love Kefalonia, as two 66 year old we have always stayed in lixouri as we find it quite flat maybe a long walk to the beach which is lovely but a taxi is not too expensive, Taverna's are very child friendly, mostly very Greek you will get the odd take away come chicken and chips but usually Greek, It's not an easy place to get to by brouchure although Tompsons were doing some deals last year we always go independantly, most of the night life is eating out they do have some disco's but they are mostly well out of the town the Apolasfi has everything you need half way between the town and the beach, July and August you may hear the music from the disco if you stay in the studios but food, pool and service are the best and children are welcomed at any age.
pojo

Dear emmski30,

I think the only place for you is Skiathos, staying in Koukounaries. Try the Sergio Apartments (First choice), Panos or Kaiti Apartments (Manos).
The Segio has pool facilities (with child area) and some rooms are air conditioned. However the other 2 apartments are close by and have a more private feel to them, both offer 2 bedroomed facilities. Koukounaries has a good beach, a bit over rated in my opinion, so try Maratha which is 1 bus stop ride away and is beautiful. The whole of the Island is accessible by bus, but Koukounaries itself has lots of choice for Taverna's, all of which are traditionally Greek. There are by the way plenty of pools to choose from in the resort.
When our children were young we stayed at Scala in Kefalonia. Although I think that Skiathos has risen in price over the years, it is comparable with Kefalonia in every way. The advantage that Skiathos has over Kefalonia is that when you have youg children you want a short transfer. I seem to remember that the transfer to scala was about 90 minutes. The transfer to Koukounaries is only 20-25 minutes.
For other sandy beaches try Troulos, Mandraki and Aghia Pareskavi.

Hi emmaski30. I would try Kefalonia or Stoupa. We went to Skiathos about 3 years ago and to be honest it wasnt my cup of tea. Some people call it 'cosmopolitan' but I thought it was a bit commercialised (they have a McDonalds ). It is the only place in Greece where we have been refused at a bar cos we had children with us

similar query to the one i have now...

One of the best resorts for young families that I have been to is Alykes & Alikanas in Zakynthos. A beautiful sandy beach. A quietish resort, but with plenty of places to eat and drink. A great island to visit. Kids love it.

We opted for Kefalonia - purely as there is a bit more for the children.

Emmski,
I will add my recommendation of Stoupa - perfect for what you describe. I will also add Anaxos or Petra in Lesbos, particularly Anaxos.

Cheers,
Jet