Substitute for Palm Sugar
I don't think you can any better than light brown soft sugar!
It has a similar taste, similar moisture content (though palm sugar varies hugely in moisture content from a thick honey texture to a solid block), similar color and caramelizes in a similar way.

An ever closer option is jaggery, which is almost identical to palm sugar, just made from sugar cane rather than palms. It is probably more difficult to get hold of though, and the difference is rarely noticeable in a finished dish, so I would say light brown sugar is your best option