Ask how many of the residents are married/long term partners; how long they've been together; how many divorces there have been. Ask how many people have kids. Have any of the female residents had kids? How long did they take off? Did they have to/get to/want to do it in a research year? Most of these questions should be able to come up naturally in the course of pre-interview dinner conversation and not be a forced, rapid-fire segment. The ones that are more family friendly sometimes highlight it in their powerpoint/presentation, show pictures of the families, etc. I would specifically not phrase it in a way that asks "How is your work life balance/How much time off do you have" etc, but rather ask for the numbers. Are there kids at the pre-interview dinner?
Ask about daily schedules. What time do you *have* to stay there until? Some programs you're out after your cases are done; some places check-out is mandatory 7pm (or whenever). What are the call schedules like? How do you pick vacation?
It wasn't something that I looked at when picking residencies, but some that I think had several residents with kids when I applied were: Knoxville, Wichita, Shreveport, Wilmington NC, Lubbock, and Youngstown. Places that I don't recall being that open about families were: Iowa Methodist, SLU, KUMC, UMKC, UAB. But a lot changes in 5 years and my memory is foggy.