So you want an evergreen (year round foliage) that isn't a conifer.

That is a tall order.

What about a green giant thuja? Native to the western united states this IS a conifer, but it does not look like a christmas tree if that is what you meant. It grows extremely fast, extremely.

Also, there is a world of unique conifers out there. Not just the plain green christmas trees spruces and firs. There are weeping varieties, golden ones, variegated ones, ones with different bark, different needle types, different cones. IF you want something that doesn't look like everything else, you literally have thousands of choices within evergreen conifers.

Just go to a specialty nursery to look for them, you'll probably be amazed by the selection.