What direction are we looking in your photo? Does it get any dappled sun or direct sun at any point in the day, or is it just shade?

Do you know what kind of trees they are? Some species (most of the maples for instance) are shallow-rooted and so it's difficult to establish new plants nearby, while something like oaks might be easier.

Would you consider planting on this side of the road/drive in the lawn or are you solid on planting under the trees?

These are oak trees. This is facing east.

I thought of the tree roots too. I've been thinking about this for awhile and the only idea I've had is to throw some forsythia in there.

I wouldn't want to cut off the driveway from the front yard by planting on the opposite side, if that makes sense.

So does it get a fair amount of western sun during the afternoon? I am just trying to figure out what will be happy enough to grow thickly there.

The obvious ideas are holly or rhododendron. Both come in shade tolerant varieties, are evergreen (so they provide a screen in the winter) and there are varieties of both that can easily reach 8 feet. Rhododendron give you the bonus of flowers, and holly give you berries for winter interest. On principle I like the native American Holly (ilex opaca) which is shade tolerant gets way over 8 feet, but for that space you might want a smaller variety.

Also...can we persuade you to plant something across the street from the neighbor's trees?

This area does get some sun, but of course being under the trees, not a lot.

Edlincoln, we will plant on the other side of the driveway eventually (but nothing tall). It's hard to see in the photo, but the paved section going down the photo is part of a circular driveway.

We would like to remove that first before planting on that side. Practically the whole front yard is paved, I hate it!

Ah, I hadn't thought of small trees! That adds some options

If you layer things in somewhat, it will give a more dense effect. If you put some things back along the stone wall they may get some eastern light, and the ones closer to the western edge will get western light. Also think about the placement to best block what you don't want to see; check out the view from those spots where you will be most likely to be viewing this area.

Dogwoods are a great suggestion, either a disease resistant cultivar of native Cornus florida, or Cornus kousa, or native Cornus alternifolia (pagoda dogwoo) which have different looking flowers from the other two. There are both green-leafed and variegated versions of all of them, though the variegated types tend to grow more slowly. Some other smaller shade-tolerant trees include hornbeam and hop-hornbeam. Flowers are interesting but less ornamental.

Mountain Laurels will grow well in shade; just choose a large-growing variety.