Is the baby in a separate room or not? Do you have a good rocking chair for feeding, and if so, is that chair in a separate room? Do you have a guest bed? Can you get back to sleep easily? What is the work situation for you and your wife (commute, hours, her going back to work or not, etc)?

All of those things come into play.

For me, I loved the quiet time to just sit and hang out with my girls as they had a late night meal. I would get in the rocking chair and talk to them a bit. And as they fell back asleep I would read stuff on my phone. I know of other people who studied or did some work in the middle of the night.

But I knew that my wife was physically recovering from the births and that she was taking care of the girls all day long and needed her sleep. She also needed to know that she could trust me to help out. We still had some silly fights due to hormones and tiredness in those early days. But it is a team effort. So if you need to sleep in another room a few months and set an alarm, or just need a night time hobby, try some new things and embrace the time alone with the kid. It ends quickly and they grow so fast.