I would recommend a Skyrocket Juniper. It grows up to 15' x 2-3' wide. Hardy in zones 4-9.
You also might consider putting up a 12' high chainlink fence and then growing some dense evergreen or semi-evergreen vines on it.
Hope this helps.

Here is a link that might be useful: Sooner Plant Farm

I should add Juniper to the list of plants we don't like :) I don't know the right term, but we don't like the looks of arborvitae or juniper or similar.

We can't build a fence, trellis, etc. higher than 6 feet near the property line. Otherwise we love vines and would be doing something like that in a heartbeat.

I don't know the right term, but we don't like the looks of arborvitae or juniper or similar.

I'd interpret that to mean you don't care for needled evergreens, aka conifers :-) That's going to limit your choices considerably as very few broadleaved evergreen shrubs - like the holly - will achieve the height/width you want and are going to be sufficiently hardy for you. And a whole bunch of conifer choices would (some with shearing).

It may be your best option is the bamboo. FWIW, it should be quite successfully contained with a proper root barrier properly installed but a manual root trim around the border on an annual basis will keep spread very much in check.

Just want to say that bamboo is a nightmare unless you don't mind it spreading (I have heard of clumping bamboo, but don't trust that it really won't spread eventually). It is pretty much impossible to contain. I don't know what kind of barrier that is, but if there are any seams that are the least bit weak, the bamboo will get though. It took me 10 years to get rid of the bamboo in our yard (PO planted it). It will return at some point since it got into the woods behind the yard. It killed several small trees (blocked light and took all water and nutrients I think) and everything else in the yard where it was. I am still trying to restore the garden to a native woodland space. I have heard horror stories of it breaking through concrete. A copper barrier might work, but that will be very expensive and you do need to dig down two feet or the roots will just go under and around it. Any other barrier material will not be effective from my research and I have done a lot. One landscape architect's response to my question of how to get rid of it was "Move!"

Try Henry Field's Seed & Nursery Co. under shrubs,hedges,and grasses find "tallhedge". Gurney's also has them sometimes. I have had mine for 15 yrs. Not an evergreen, grows 10ft - 12ft tall and 3ft wide. Best of all I have never had to trim them.

Clumping Bamboo or properly contained/installed Bamboo sounds like a good choice. My concern with trying something like a tall/slender holly would be snow damage. Don't you get a lot of heavy snow? I would think that snow damage on the Bamboo would be easier to manage (will either spring back or damaged canes would quickly be replaced by new growth).