We usually keep babies with moms at all times. Unless, of course, there are any problems, but if baby is healthy, no need to "transition" in another room -separate from mom.
Babies are assessed in mom's room, weighed, measured, given meds, bathed, rewarmed, and placed back in mom's arms. She does have the option of having any of the above done in the nursery, but most moms like having it all done in front of them.
Nurses who have come to work at our facility after working in larger hospitals with separate nursery, postpartum, and L&D units have a real adjustment period, but usually end up admitting that it does work well and really is more mom and baby-friendly.