I had my 1st at a different hospital and she went right to the NICU so I'm not sure how it worked there but the hospital where I had my other 3 is exactly like the movies.. big nursery, window all that jazz, you have the option to keep your newborn with you during the night. I did. I just wheeled them into the bathroom with me when I had to shower and stuff.. just like I would have at home. I honestly wanted to leave right after I had the last 3. I was fine with in a few hours. I would have got more rest at home too. The nurses come in every few hours to wake you up anyway. I got no rest there. At home I could relax. I could see why people choose to have their babies at home (with a midwife) DH was set against this!
At my hospital, many night shift nurses are elated to have a patient that wants her baby to be in the nursery all night
I work in a huge, inner city hospital that does the most deliveries in the area, so yes, we do have a lot of nurses. Twenty years ago when I started, we did have an average of 8-10 couplets per nurse at night. Now, thank God, we average 3-5. We have a huge high risk population, so we have all kinds of complicated patients on our floors, so having a low nurse-to-patient ratio is a must!
We have a seperate anti-partum floor whose ratio used to be 4-1, but even that is 8-1 now. ( I have a friend who still works there.) 
The nursery was not supposed to be used much at the hospital where my dd was born, and I was VERY happy about that. I just wanted my dd with me the whole time. However, I had 31 hrs of labor and then an emergency c-section, so they told me she could not stay with me. 

With our twins, they went to the nursery at night from 10 - 5, even though DH was with me. It was nice to be able to get some sleep before the nightmare sleep deprivation began once we got home. I had a c/s with them, and I don't think a woman recovering from surgery should be expected to care for a newborn 24/7.
I dont remember what I did with my 2nd daughter it was almost 7 years ago