Plenty of students apply to both Northwestern and Chicago. Why? Because the overwhelming majority of qualified applicants would be just fine, and have an enjoyable experience, at either, regardless of their differences.
Valuing prestige (while also wanting to be closer to family) is smart and provides tangible benefits.
For the OP, while I think you would really enjoy Northwestern, Chicago or Duke, if being closer to family is the top priority, gunning for schools with transfer acceptance rates that often dip down to around 2% is not likely to solve your problem.