It’s somewhat difficult to illustrate your question with the image you’ve posted. It’s really just a vacation snap with no real creativity behind it. However, it does tell a story. It says, "We were here." So with that in mind I'd expect the background to be in focus so I can see where they were. Like most snaps, however, its common place to have everything in focus.
Assuming you are trying to be creative what's in focus all depends on what you are trying to achieve in your photo; where do you want to draw the viewers attention. For example, in the first image below I hope the story conveyed to the view is something like “sisters looking out over the city skyline.” Hence, since the skyline is a part of the story it should be in focus. Being in focus helps draw the views attention to the same skyline the kids are enjoying. It’s an important part of the entire image.
On the other hand, the second image below taken in the same place, is trying to draw the viewers attention to something completely different. In this case since I want the viewer to notice the girl and the visual affect so I don't want the background in focus. The background however is important because it set the scene and mood of the over all image. In this case the background places some context to the subject but if it were in focus would just be a distraction. In addition it would be a boring picture if the background was just some colored backdrop.
So there you have it. I'm sticking my neck out, especially here on DPR ;-) by using my own images but I hope they actually do demonstrate my thoughts on the subject.
Ultimately, it’s the viewer who will decide if they like the image or not, but it’s the photographer who should decide what should and shouldn’t be in focus. There are really no hard fast rules other than the creativity of photographer and that is what makes photography an art form as apposed to just another recording media. Experience will help dictate what works and what doesn’t work as one is trying to be creative.
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Rob Kircher
My Stuff:
http://www.pbase.com/rkircher