Dear Readers: your advice, please! Or, whether or not to unleash the not-so-secret weapon

With kind thanks in advance.

Dear readers, I have a quandary.

I am applying for a fellowship in Infectious Diseases; that is, two years of additional training beyond my residency.

I have been called reasonably intelligent, occasionally even bright, and have decent evaluations.  I have (I think?) good letters of recommendation.  I have strong board scores.

I stand a decent chance of being accepted to stay on at my current institution, and life is wonderful here.  Husband and I live within a brief walk of my parents, grandparents, aunts, uncles, etc.  Our neighborhood is charming and we own our home.  And I was always taught that family is the most important thing.  Plus, we may perhaps? have a little one on the way, though I still hesitate to believe it.

Here, then, is the debate: I have a not-so-secret weapon at my disposal.  His name is _____, Division Chief of Infectious Diseases and internationally-renowned expert in the field.  If ____ makes a call, I could go Elsewhere and train and Big Name Universities.  At least, I am told so.  If he tells you to take a candidate, you take the candidate.

Thing is, if you unleash The Division Chief, it is binding.  You rank the Big Name Universities first on your match list.  You can't have someone make a call and then change your mind.

Now, training at a Big Name University might be a life-changing opportunity.  It has been known to Open Doors.  But what if the doors I wish to open are those of a home down the street from my loved ones?  And how would I effect child care if we do have a baby and we live far away from my family?  My family is what is dearest to me in life.

Thoughts?