Here's a solution, which I'm fairly certain works as intended (but we saw where that got me last time ;)

sub path {
(*g,$f,$t)=@_;@s=map[$f,$_,$r{$_}],keys%{*r=$g{$f}};
push@s,map[@p,$_,$d+$r{$_}],keys%{*r=$g{$n}}
while(@s=sort{$b->[-1]<=>$a->[-1]}@s),$d=pop@{*p=pop@s},
($n=$p[-1])ne$t;@p
}
[download]

170 characters... Yikes! I'm sure someone can do better than that!

Update: Hey, I don't need to do that complicated initialization of @s!

sub path {
(*g,$f,$t)=@_;@s=[$f,0];
push@s,map[@p,$_,$d+$r{$_}],keys%{*r=$g{$n}}
while(@s=sort{$b->[-1]<=>$a->[-1]}@s),$d=pop@{*p=pop@s},
($n=$p[-1])ne$t;@p
}
[download]

142 characters!

Update:

This solution will be very slow on the NYC to SF test case, because it gets stuck moving back and forth between Chicago, Cleveland, and Detroit for a while, because SF is so far away. However, it will find the solution eventually.

Of course, this could be fixed by preventing the code from moving back to a node that has already been visited, but we're optimizing for character count, not for speed of execution! ;)