Agree with mdizzle and app123456 - not sure how one rotation in a region 'opens up' the whole region. Places largely won't know where you did aways until interview season. Away rotations, if you do well and are a good fit for a program, can greatly facilitate getting a spot at that program regardless of geography.
One story: had a friend from one area of the country, grew up there, but the folks had moved and ended up graduating from high school/college/med school elsewhere. Despite doing one away rotation in the area, as interview invites started going out, none where forthcoming from the area where my friend wanted to do residency and have a practice. In a bit of a panic, sent along a supplemental letter and got some phone calls made to endorse the deep roots and desire to be in that area longterm. All worked out in the end.
If anyone is looking for ways to beat the geography and somehow get 70 interviews all over the country despite having grown up and schooled in only one area of the country, good luck. If I were a program director I'd be suspect that you are just interview hunting and not legitimately interested... if you were, you'd have done an away rotation. Otherwise you probably won't rank the PD's program high, or if you do its only because it is among your only options. I think all PDs, regardless of program, want residents who really want to be there. This is just another reason why the shotgun approach to residency applications doesn't work too well in my opinion. Better to start early and be as good an applicant you can to the 20-30 programs that you really know you'd like to spend 5 years at, for geographic/personal/professional reasons, and pick some selective away rotations at the programs where you think you might get overlooked for whatever reason in the pre-interview stage.