Den Haag (The Hague) is a cool place for kids. Great touristy beach and a neat miniature city. Lots of museums and the Royal Seat of the Netherlands. You can do all your commuting in Holland by train and tram so you won't need a car.

Another choice is Munich which has lots to do in the city, and its a short drive to the fairytale castle district. It's filled with museums including several technology museums and the BMW museum.

Of course there is Paris with Euro-Disney.

The French Riviera is quite popular with families and there is lots for the kids to do. There is a neat amusement park and marine world near Antibes. The ocean air blows the smoke clear at the outdoor cafes. However it is quite crowded with tourists in the summer.

The Greek Islands would be good for the kids. If you go to Crete, it's spread out enough and most everything is outdoors so you won't have to worry about smoke.

Driving around Italy and visiting all the old places can be interesting for the kids. But then again, summer is very dusty in the old cities which probably wouldn't be good for anyone with Asthma.

Last but not least, I would suggest Prague and the Czech countryside. I did find a non-smoking restaurant there called U Svalta Ducha.