And this is what I look at:

Love the picture of the trash can. If you don't have deer I'd recommend a Densiformis yew (Taxus x media 'Densiformis'), grows well in less than full sun, dense, gets to about the size you want, and if it gets too big it tolerates pruning well.

In spite of the fact that it would make one wonder how people can be so thoughtless, the new neighbors may be concerned about so many other things that they are actually oblivious to their causing an eyesore for you. I would give them the benefit of the doubt and ask them in the nicest possible way, explaining how the garbage cans are front and center for you, if could please move them to a screened in area. (Before doing this, check to see if neighborhood regulations require them to conceal the cans.) They may comply (with or without a huff) and the problem may be over without your making any modifications. If they say no, then you know squarely what you're up against and can take the appropriate measures.

I like both your suggestions. Ckerr, the Densiformis yew does seem like a good choice for that area. I am not that fond of the Rose of Sharon. It is a good one---it doesn't produce seeds---but most of the blooms face my neighbors anyways because that is the direction of the sun.

Yardvaark, what you say makes sense, but I don't feel I can mention the garbage cans to them. I don't think they have any idea that we don't like looking at their cans. They can't put the cans on the other side of the house and their garage is full. I am OK with removing the Rose of Sharon.

"... and their garage is full." There is the red flag.