With your location I would guess your hardiness zone is 6 or 7.* With that little bit of sun I would call it part sun.* Japanese maples come to mind as most don't like full sun.* There are upright and dwarf spreading ones that sometimes look more like shrubs.* Dogwoods also might be a good choice as well as the star magnolia aka Magnolia stellata.* The saucer magnolia aka Magnolia soulangiana might also work.* Look for a later blooming one if you are in zone 7.
You don't say if you want evergreen or deciduous or don't care either way so I selected those that came to mind first.
With no disrespect to Natural Cat, I'm not sure Rhododendron 'Yaku Princess' will be tall enough for you.* They sure are lovely when in bloom.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.