Hi, I would recommend Koukanaries. It is a very flat resort with only a slight slope leading out of the eastern side of the resort. All of the accommodation is on flat ground, the only exception being the Skiathos Palace which is on a steep hill about a mile out of the resort itself.
The beach at Koukanaries is excellent and very safe for bathing, although it does get very crowded at peak times. Aghia Eleni is just around the headland and is another excellent beach and is worth the twenty minute walk to get there. It is a lot less crowded and still has a taverna for the all important drinks and snacks! The sunset is stunning from here too.
All of the hotels in the resort have pools and air conditioning and some of the apartments have pools too. (i would assume that nowadays all but the most basic rooms will have air con.)
As with most hotels and apartments in Greece, visitors can use their pools provided you buy a drink at their bar. We usually use the excellent pool at the Caravos hotel, even though our own hotel had it's own pool!

Hope this helps!

John

Thanks for that John. We dont go in peak season anyway so it sounds ideal for what we want.

Great advice by keffadict