Worst thing to do with a kid could be taking it to a museum as large as the Louvre. I think there’s a good reason why I usually skip the visits of museums while traveling. So I don’t think it’s more appropriate to take them to a venue that could be seen as a the cloud of the art galleries.
There where even lots from Zurich whom I’ve never heard of. Despite all these drawbacks, there are some nice points to mention, making you wanna attend the next one, no matter if in Basel or Miami. You can see a lot of art. From photos to sculptures, just everything and most of them with pricetags, if they are publicised, preserving them from hanging on my walls.
Second and best thing: Art Basel is quite sexy. Most of it comes from the art, I think, and the other part from the dialect they use to speak in the area.
And all those people from the galleries with their state of the art understanding of the future and mindblowing individuality are using their unique brand to stay where they are. Has to be quite boring to be around so many look-alikes for them. But for those few days they somehow manage it quite good.
Afterwards a drink, in a bar overlooking the town, paid for with the money you won while gambling, perfect.