Link:
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On the south side where the 1' drop is, is there a retaining wall? If no retaining wall, is there an erosion problem? How steeply does the land drop off?

there are a few garbage pieces of wood, but nothing really substantial. No erosion problems; the pictures will explain better than I can!

Here is a link that might be useful: Pictures

Install a large paved (brick, flagstone, whatever) sitting area, and some shade-tolerant plants of mixed heights around the perimeter. Ferns, columbines, lily of the valley, etc.

Trellis with shade-tolerant vine for privacy. Put the plants so they block that drop-off.

You will be surprised how popular the back yard will be when you can sit there, eat there and hang out there. Make a summer outdoor living area.

Lazygardens - sounds awesome!

Can anyone point to a good resource for a layout?

I wouldn't want to look at cars when I'm sitting in the garden, so I'd try to block that view as well, maybe with a fence or trellis. (Making the asphalt area smaller is probably not an option, so I won't even start on that).
There are two possible locations for the seating area - one near the house, one where the table stands in the picture. Try sitting down in both locations and imagining how it could be like.
Book recommendation: Andrew Wilson - The Book of Plans for Small Gardens, 2007, this might be helpful in a narrow space.

I'd try to block that view as well, maybe with a fence or trellis.

Re. timbu's comment, keep in mind that you don't have to fence the entire length of the asphalt, merely enough to block out the worst views from the seating area. That might well be only ten or fifteen feet. And I would think it doesn't need to be more than four or five feet tall.

While you're sitting down in the different locations, make a fence mock-up with some bamboo stakes (maybe with sheets clipped to them at various heights).

We love our cars and wouldn't mind sharing a back yard with them, in fact for people who like to wash, detail, and otherwise fuss over their cars, such a yard would be perfect. Even if you don't love your cars, I wouldn't subdivide the area with screens, you have to get in and out of the cars after all, load and unload them too.

If they do compromise the enjoyment of the yard, maybe you can park them further from the house.

KarinL

Karinl, wow, do you drive a Model T or something?

Hah, not a model T, but a selection of vintage vehicles of various kinds is always part of our lives. This is the kind of yard where I can just imagine my husband and a group of his friends gathering with whatever toys they've decided to convene around - having a table and chairs to the side would just round it out perfectly. And although DH and buds are getting to be geezers, there are plenty of younger equivalents.

However, I see I had the driveway backwards the first time I looked at the photos, and the cars could just be rolled back to beside the house for the yard to be enjoyable without them. In any case, I think a divider of any kind would reduce driveway function to mask what is to me either not a problem or one easily resolvable by other means.

You could consider resurfacing the driveway and cleaning up the edge. That to me is the greater eyesore, not the cars on it.

I think your basic plan sounds great. Honestly, if you just get a patio set and put in on the grass, you'll be 60% of the way there (with respect to decision-making anyway). Once you're sitting out there, as Timbu says, you'll start to realize what you want to do from there.

Also, if it's too shady, evaluate the tree scape and decide where those trees are in their life cycles and if they're in the right places, and whether you need to start making a replacement plan. Thinning some of them might also be an option.

KarinL

Layout ... landscaping is just like arranging furniture in a house.

Imagine you are using the area for outdoor dining and lounging. Bring out some chairs, or borrow some lawn chairs and start pretending to do whatever out there. Use boxes for furniture if you have to.

Figure out what the traffic flow has to be, from kitchen to table for eating, minimize people cutting through the lounging area with trash cans, that sort of thing. For any landscape, there will be good and not so good places for things to be. For example, walking past the poopy dog yard to get to the outdoor dining area is not good.

When you have the activities and furniture figured out, get some bright-colored string and start laying out the boundaries of the activity areas ... for example, your patio has to be big enough for the table and chairs and lounging.

Then start figuring out where you need to block views: Sit where you will be sitting and look around. Where do you need to block things? Does it need to be all-year or just summer. then look for a plant that fits the space.

Here is a link that might be useful: Create your own landscape design