I don't want to see my neighbors' back deck when I look out my bedroom's northern window so I hit up the garden store to get some privacy shrubs. I ended up getting and planting three Emerald green arborvitae. They should grow around 12 feet tall and around 6 feet wide so they'll eventually block my window. I guess they grow just one foot a year, but maybe I'll get lucky and they'll grow faster.
From the picture, you can see they'll get some sun which should help. The acidic needles should also keep that yard mostly free of weeds.
I think my property line is actually another ten feet from the shrubs, but there are already a lot of trees there. I'm not sure why the previous owner did not extend the fence down this part of the yard. Maybe he didn't want to cut down any more trees than necessary.