Argthtjtr

As long as reportedly Americans commonly designate an area of land, usually planted with plants, trees, flowerbeds, etc., adjoining a house as a yard (front yard/backyard); and a plot of land used for the cultivation of flowers, vegetables, herbs, or fruit as a garden — what do Americans call what is referred to by the British as a yard, i.e. a piece of open ground, usually paved or laid with concrete or gravel, and often adjoining or surrounding a building or buildings?

Is it also commonly designated by Americans as a yard (front yard/backyard)? Or as a courtyard? Or is there another term to it?

If indeed it's also called a yard, isn't there — if context is unclear — any chance of ambiguity or misunderstanding as to whether it's a planted area or a paved/concreted/graveled one that one is referring to?

A yard is simply [AHD]

A tract of ground next to, surrounding, or surrounded by a building or buildings.

What one expects it to look like or to be used for depends on the building in question, but yard as paved open ground adjacent to a building certainly survives in American English in terms like schoolyard, lumberyard, barnyard, stockyard, or junkyard.

If the building is a "single-family" residence (i.e. detached or semi-detached), then one usually distinguishes between the front yard, situated between the house and the road, and the backyard, which extends behind it to the edge of the property; telling children to stay out of her yard is ambiguous and requires context to determine which yard is meant. It is possible to say side yard as well, although where such land exists it is usually only a strip to allow access, and not usable open space. The analogous terms in BrE appear to be front garden and back garden.

But what any of them looks like or is used for should not be generalized. There is huge variation in their size, orientation, and maintenance across all of the climates, social customs, local ordinances, and neighborhood ages to be found in the U.S. The television sitcom suburban house on a quarter-acre plot with a manicured front lawn and treehouse in the back is not possible or practical in a very large swath of the country.

The British sense of garden for any cultivated land next to a house is not used, except perhaps in New Jersey's nickname of The Garden State. Rather, a garden is an area of the yard (or of flower boxes or planters) where specialized plants are grown: flower garden, rose garden, vegetable garden, herb garden, and so on.

A courtyard is an architectural feature [AHD]:

An open space surrounded by walls or buildings, adjoining or within a building such as a large house or housing complex.

One cannot simply lay down a strip of pavement beside the house and call it a courtyard without attracting some ridicule (n.b. an icicle crashing through your roof does not give you an atrium, either). A courtyard is larger than a patio or lanai, and probably larger than a terrace, and would be a feature of a large house or a multiple-unit dwelling.

How I use and have seen these words used:

front yard - area from front of your house to curb.

back yard - area from back of your house to the back of property line, which sometimes has a fence.

side yard - area on either side of your house.

yard - front yard, back yard, side(s), all combined.

garden - specific area in a part of your yard that is used for planting groups of flowers, fruits, or vegetables.

lawn - sometimes is used in place of yard put really refers to part of yard that has to be mowed (grassed areas). You can mow your yard or lawn and it is the same thing. People don't think if you say that you are mowing your yard that you are mowing over the garden section.

courtyard - normally this refers to a common area at a hotel or apartment building that several units would share. It would usually have places to sit, eat, and sometimes cook. I guess it is still used at bigger houses (mansions) as an area that is segmented from the yard for the purposes mentioned above. It would usually have a fancy fence around it and maybe garden features inside.

grouping of trees - we just call them trees. I have 27 trees in my front yard. I don't call them anything special.

laid concrete or gravel - we have a patio, porch, and a driveway that can be paved. Any other rogue concrete would be referred to as a slab.

For this specific area:

a piece of open ground, usually paved or laid with concrete or gravel, and often adjoining or surrounding a building or buildings?

I would call it a "patio":

A paved outdoor area adjoining a house.

Some of the other suggestions are good but the benefit of "patio" is that it implies that it's a solid, open surface.

It's generally where we place tables or chairs for lounging or dining in our yard.

Here's one with stone:

[from: http://www.nobis-eng.com/wp-content/uploads/2015/02/patio-contractor.jpg]

Or one with gravel:

[from: http://patioideasite.com/wp-content/uploads/2015/02/pea-gravel-patio-design-pictures.jpg]

you answered your own question:

courtyard

That's at least what we called "a piece of open ground, usually paved or laid with concrete or gravel, and often adjoining or surrounding a building or buildings" in the New England area...

edit: and yard can either refer to the front or back yard...

"Yard" is usually clear in its context, however, not always unambiguous. "Prison yard" brings to mind an enclosed, paved surface, for example. "Play yard" or "school yard" can be both, hard surfaced and grassy. "Courtyard" is usually considered a somewhat enclosed area, partially walled off.