I'm very fortunate that my parents live in the same city. When I go in labor, we will drop DS off at my moms (same neighborhood). If I am to be induced, same plan.. drop him off at my moms.
As long as it's not the middle of the night, she will bring him up to the hospital close to the time the baby is going to be born. She will also be bringing him up there for visits.
I'm not sure yet if she will stay at our house or her house at night time yet.