Shrine isn't a term commonly used in Asatru. But I get what you're aiming at.
I am currently a reluctant apartment-dweller with limited personal space and none of it outdoors. I have dedicated a wall in my bedroom as altar space and have a large and rather nicely decorated piece of wood shelving (language is failing me here, as it is actually a series of three shelves enclosed in a frame... but I don't know if that sort of thing has an official name). In any case, I jokingly refer to it as my "Walter" (short for wall altar). The top level is for gods and other divine powers... here I keep my Thor's hammer and statue as well as some smaller items. The second is for wights and ancestors, with a special "Norn cauldron" representation in the center. The third level is more of a personal level concerned with living kin and general items that connect me with general aspects of the faith and culture such as rune stones and a family heirloom or two.
Now my kinswoman, who has land that is expected to remain in the family, has dedicated a vie in her garden. It is a pillar of stones that have been piled above a specially dedicated hoard, with a flat stone on top where offerings can be placed or poured out.
I would agree wholeheartedly with what others have said, that function and practicality take precedence over form.