Several social media sites claim a high degree of granularity with regards to "who can see what", but it seems to me that the granularity for the "who" part is typically very poor. When you publish/upload something, the control over "what" people can see is very fine -- you can define it for every individual item. But the control over "who" can see those things is usually limited to "the whole world", "friends" or "only me".
Can you point out any social media sites that provide a wider range of options than that?
This is a really good question. Having my background in content management environments it is a real issue when you move the environments like Facebook, Linkedin and Ning as they generally have very poor permission structures. I suppose it is a result of "one size fits all" approach to cloud systems.
I think Linkedin has subgroups that might help you. Otherwise you will need to take a look at some of the customisable tools that support Social Media tools. I use a tool called eZ Publish for this along with Plone but there are other tools. Just checkout resources in this site to find a few.