Most hospitals operate for 24 hours a day, and we don't generally see all that much about what they are like in the overnight hours — that is, when a medical show even goes out of its way to differentiate time of day, with most of them just taking place "whenever." That's the hook of NBC's "The Night Shift," which is all about the staff that work at San Antonio Memorial Hospital when the other doctors and nurses get to go home and go to sleep.
Beyond that, "The Night Shift" makes great use of its Texas setting and feels very accurate to that part of the country. A lot also revolves around veterans, with the staff comprising a lot of ex-military personnel who were in Afghanistan in addition to many patients being vets as well. As such, there are a lot of storylines that deal with PTSD and other struggles that people have after they return from military duty, which is territory that most medical shows don't touch outside of the occasional episode specifically dedicated to that.
"The Night Shift" was canceled after four seasons, but it's all available on Netflix at the time of this writing.