Many of the larger evergreens can be limbed up to get an open shape at the bottom. Hollies, viburnums, 'Little Gem' magnolia (but I hate to suggest it for that species/cultivar - I like them growing to the ground), Sweetbay Magnolia (M. virginiana), wax myrtle, mountain laurel would all be possible. As an evergreen that shouldn't need to be shaped, there are: Italian cypress, 'De Groot's Spire' arborvitae, also 'Emerald Green' arb., a clumping bamboo (NOT a running one), or an Irish Yew (may be too slow growing) - all of which grow more as columns than as pyramids. There are other columnar or fastigate evergreens as well.

You could have a look at the various Arbutus and see what you think. I don't know if they would suit your climate but they are attractive evergreens with reddish bark, racemes of white flowers and edible (but not tasty) strawberry-like fruit. Another one to consider is Laurus nobilis, bay, which will grow into a tree, albeit rather slowly. Another thing to bear in mind is that you will need to choose your plants carefully for the flower bed below this tree. Shady beds below hungry evergreens can be a pretty harsh environment for plants. But there are some which will manage there.

Perhaps Virginia Pine or Japanese Black Pine. Both of these are somewhat smaller trees that don't always strictly maintain a conical shape. The lower branches typically fall off or can be pruned as tree grows.
Another thought is decorative junipers or perhaps an Arborvitae of some type. These might cast too heavy shading for a bed underneath.

Some of the upright hollies such as 'Oakleaf' will give you dense evergreen screening, and won't get so darned wide, which will allow you more room in your bed for other plants. If when you say 'tree-shaped', you mean spreading up top - that will be a detriment to growing things underneath as they will cast a lot of shade onto your perennial bed -- unless you like growing shade-loving perennials like ferns, hosta, etc., it seems to me.

You may also consider Photinia, Carolina Cherrylaurel 'Bright n Tight', Japanese ligustrum, Chinese evergreen oak, Holly osmanthus, Camellia sasanqua, Chindo viburnum, Leatherleaf viburnum, lots to choose from.

I think Osmanthus fragrans would be good there. Mine is about 13 feet tall after 3 years (I bought it as a 3 gallon). It is very full at the top (especially since I snipped some off last year). Very fragrant!

Chindo viburnum has not been such a good looking plant for me. Grew fast and left a sparse area in the middle (which I hope will fill in eventually).

I would not recommend Ligustrum to anyone in Virgina - it's considered an invasive plant and there are better things to choose from. I don't care for the flower's smell either.

Sort of depends on where in Virginia you are. The list I gave would work in Northern VA. I don't believe Ligustrum is invasive up here. Never have seen it spread, but I could be wrong. Perhaps in Tidewater VA it's another story. Osmanthus fragrans is not bullet-proof hardy up here. Wish it was! Fortune's Osmanthus is slightly hardier. There are some absolutely beautiful Chindos in the Williamsburg area -- very dense and conical. They take time to fill in and may need some initial pruning to shape them up.