Thanks for asking about this,
@kjj17. My husband and I don't have kids yet, although we do have a dog, who seems to think she is a person! Your question is something a lot of med and pre-med students--single students and those in a serious relationship, younger students and older ones, women and men--think about and, at least here, talk about, too.
I wish there were a blueprint for the ideal time to have kids in relation to medical training, but, unfortunately, I haven't found anything like that yet. What I can say, though, is that I think it is more feasible to start a family here than most other places. The reasons are pretty straightforward:
1) flexibility in the curriculum, especially with 3rd year
2) the low cost of housing--a two or even three bedroom apartment here in Durham will cost less than a studio would cost many other places.
3) the low cost of daycare--in many of the cities where we looked, daycare was simply unaffordable even after it was "pro-rated" based on our income. Very generally speaking, daycare in Durham costs about half or less of what we saw in many other cities.
4) a supportive environment--from the faculty, to the advisory deans, to the other students
5) a critical mass of students with kids--off the top of my head, I can think of seven MD or MD/PhD students here at Duke with kids, but there are probably more.