I feel that you are not telling us the full story here.
I get the feeling that your viewpoint on your career (perhaps even on life opportunities in general) may have prematurely crystallized. Your comments above betoken a naive trust in a self-chosen 'orthodoxy' - albeit one occasionally supported by instances where a supervising academic may act with immoderate or ambiguous interest where an ex-student is involved - that isn't really the norm at all.
Let's get something straight here.
You're not going to get any interview or appointment on the back of playing your supervisor - however subtle an operator you may think you are. Even if you did it would be so much the worse for you: the high expectations of your new employer/supervisor and the likely lack of commitment on your own part having got the opportunity without real personal effort would soon lead to disappointment on the other side. Then where do you go ?
So, you may have read that Prof X suggests some internship/fellowship to student Y but this is very much the exception rather than the rule. And God help you, if you think you can specify the location of a job that you are prepared to consider your professor recommending you for then you are in cuckooland and damn well you know it ! On the last question, I know that some colleges appoint many of their ex-undergraduates and many of their doctoral students to their staff. As other posters pointed out, sometimes there is a brief low-level sojourn at another college until they 'return' to their alma mater. But look hard at the quality staff in your own college, even your own department. Not just faculty but those in support positions. There are always lots of foreigners among this group. In my own experience, the only genuine educators I met in my own country were foreigners. They were the ones who broke the old mold of bad curricula, boring lectures and mindless assignments and projects. Having got their positions mostly through familiarity with senior faculty, the native staff were naturally unwilling to appear disloyal by pushing for changes that they may privately have favoured. So I don't think it serves the students well to have faculty who are ex-students of that same college and certainly not also natives of that city. To me, a university's ranking for educational quality is synonymous with its commitment to new blood faculty appointments - the alumni just don't want the social hassle, if they care at all.