At what height should a painting or artwork to be hung on a high ceiling wall?

The height artwork is placed on the wall is determined more by the use of the room and the people who frequent it than by the size of the wall.

In most rooms the artwork should be hung at approximately eye level (for were you are most likely to be viewing it - standing, sitting, reclining).

If for example you are hanging artwork in an entrance area or hallway, the paintings should be higher (because you will be viewing them standing) than if you are hanging them in a dinning area or living room (where you spend most of your time seated).

In stairways the artwork should be hung in a progressively elevated manner (like the stairs). This gives the viewer more comfort and ease of viewing.

If you are doing a large display of many different sized paintings it is best to pick one or two "anchor" pieces and hang them at the optimum height, then make a pleasing grouping with the other pieces at varying heights to keep the viewer's eye moving through out the display.

There are some people who like to hang one or a small grouping of paintings over the sofa in the living room, and this works well as long as they are not hung so high as to make your neck ache to look at them, nor so low, they are easily bumped by the heads or arms of people sitting on the sofa.

Single pieces hung over mantles should have ample room beneath them so that items set on the mantle do not obstruct the subject of the painting.

In bedrooms, many people hang artwork over the head of their beds, the height of the headboard will determine the placement of the artwork... however if the headboard is especially tal you may want to choose a longish horizontal piece of a collection on smaller pieces that can be arranged in a horizontal manner.

One of my favourite placement for a painting was in my grandmother's bedroom, she had a small petite-point piece in an ornate frame hung at shoulder level (when seated) next to her favourite reading chair. I have often borrowed that placement when trying to create a "personal space".