They have different meanings. I can't still see the artist.... means you could see the artist in the past but now you cannot. Perhaps he has moved. I still can't see the artist ... means you have not yet seen him. Perhaps if you move closer you might be able to see him. HOWEVER, we would probably reword the negative form 'I can't still see him' as 'I can't see him anymore.'

'I still can't' is the correct order.

Rachel is right. You can also use the order, "Still, I can't see the artist."