Trying to add a few more pictures but it continually stays "grayed out" even after waiting about 10 minutes. I have tried several more times to no avail. Frustrating.

What are you wanting to plant in the new bed. It seems like anything with height is going to overwhelm the back of house and walk.

How deep is the pipe buried?

Overhanging growth from the neighbor's yard belongs to you where it crosses the lot line. You can do with it as you please. Naturally, this can become a sticky situation, often because neighbors don't know that their neighbor's have the right to cut off parts of their encroaching plants. Approach it judiciously.

The pipe is buried 18 inches and is hard PVC rather than flexible. The size of the new bed area is approximately 12 feet wide by 30 long.

We wanted some plant material with a little height and width so as to give some privacy to the grill surround area that can be seen from the street and my neighbor's drive.

Still can't add any more new pics.

You may need to resize the pics down. That's the issue whenever I have that problem.

Your local city or county probably has resources for planting recommendations for rain gardens, bioswales, etc. There's often drainpipe as part of those installations so I wouldn't expect the roots to be problematic (our local lists are fine). If you're unsure where to start, try the Environmental Services department of your local city or county, your local soil and water conservation district, or your local county extension office. While I don't totally stick to their lists, they're a good starting point of local plants that will work.

As far as how close, I probably wouldn't plant right over it because I assume it's below the low point and you want water to be able to move down the surface swale. Otherwise rain gardens, etc can be planted pretty intensively.

Here is my attempt. We were thinking something to block the view just a bit and add color. Grasses to hide the utilities. Arborvitae flanking the sidewalk and some flowering bushes.

Just make sure the arbs are going in a dry-ish area. Wet feet will kill arbs super fast.

Revolutionary, do you think the arbs look bad in a pair of two flanking the sidewalk? I really like the DeGroot Spire but anything that is pyramidal and fairly narrow would be okay.

I actually wanted more arbs in the new bed next to my neighbor but with the drain and the plant material there, I don't think it is a good idea.

I am open to all suggestions!

View of back along property line. French drain terminates just to the right. Wanting to add color, interest and privacy. There is one large walnut tree to the left.

In my experimentation with small tree forms, I've see it is possible to create them with many trunks, like a thick bouquet, if additional screening is needed at the lower portions. Over time, the trunk portion can be a screening element, even without foliage. This is one in progress. As the trunks thicken, that section will become impossible to see through.

(Obviously, it is winter and there is no canopy, but with its canopy, this tree is is quite dense. It still has a lot of foliage in the lower regions because it has not yet achieved its final height ... but just about.)

Yardvaark, that looks nice! Thank you. If next to the planter box, which trees would you recommend? The planting bed area next to the box is 4 feet deep and 6 feet long.

A small, multi-trunk tree form is made of large shrub (one that gets the size one wants) and has other characteristics (color/texture/flowering/seasonality/personality, etc.) one finds desirable. If you want something only 10' tall -- ever -- a dwarf burning bush could do it. If you can't wait and would rather do a little top trimming later, a regular burning bush would work. That's just an example. There must be lots of large shrubs where you live that could be used. Avoid anything suckering/caning/side-sprawling such as Forsythia, as it would be uncooperative. It needs to be something that will develop stiff trunk. In the above picture, it's a crape myrtle. It's height can be controlled by annual "pollarding" (which is not quite the right word for that exact process on a multi-trunk tree. Beheading maybe.)

Without being too clear on all the details...maybe think about large pots or planters in the challenging areas?

Bamboo is an excellent privacy screen in planter boxes...in the ground it usually spreads too much...