I'd like to put something decorative in the circle of dirt between the mulch ring and the base of a tree. Are there any options that are considered acceptable? A thin layer of decomposed granite? Same thing pea gravel? White stone? Large bark chips that will still allow moisture and air to exchange or dry away?
There's no reason why you can't extend the mulch cover to within an inch or two of the trunk, assuming the mulch is something of organic origin, isn't too deep, and won't be sitting over any tree roots showing above the soil. Organic mulches (composted materials, bark chips and so on) are preferable to inorganic mulches because the latter don't improve the soil in any way, whereas something organic does, as it rots down.
You don't say what tree it is, but whether it is deciduous or evergreen, there will be leaves (or needles for conifers) and other debris from the tree which will collect over any type of stone, and that can be difficult to manage. Whatever falls onto it will rot down; trying to remove wet leaves is particularly difficult, even removing dry leaves will disturb the layer of stone, and small needles will be impossible to remove.