My recommendation for somewhere different would be Croatia. Europe is still warm in September and there will be fewer crowds. I travelled to coastal Croatia many years ago and it was beautiful. More recently I had friends who spent 6 months cycling in Europe and ended up in Croatia for about 7 weeks, which they really enjoyed. As soon as you get away from the coast, it's not touristy at all they said but everyone was friendly and helpful.
I have no experience travelling with children, but it sounds like you are looking to go somewhere with a child as opposed to a child-centered destination.
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