@Flavabobble
I love Skiathos, and recommend it at every opportunity. I'd go self catering, spend the days at the beach and eat out all the time.
I also bloody love Skiathos. Stayed in Skiathos Town, and toddled around the area. Top tip is NOT to get the bus to the big beach in Koukounaries. I mean, it's a nice beach, but the stress of ramming onto the hourly bus took away the pleasure. We hired a car for a couple of days, which was much more chilled. (About E40 per day, from memory.)
Other favourite place is Naxos, but again, not the beachey/resorty part. Naxos Town has some fantastic hotels and restaurants, and we've stayed at Ikaros Studios ikarosstudios.com/ (Nikos is a marvel - and I've NEVER stayed anywhere so clean anywhere in Greece!) twice - and there's ace beaches within about 10 mins walk. Not super busy either; lots of Greek people go on hols to Naxos. Again, we hired a car for a couple of days, and went to other beaches, and into the mountains.
Finally, if you're looking for a super safe beach place for kids, I'd recommend Alikanas in Zakynthos. The beach shelves so gently, and the water is so clear and warm. You might even be lucky, and see turtles swimming by.
It's years since I was there, so I can't recommend a hotel, but there were a few right on the beach. It had a fair amount of restaurants/shops/bars too - and a regular bus to Zakynthos Town too.
God, I love Greece.....