Most people stay in the hospital 1-2 days after a vaginal delivery and 3-4 days after a c-section.
Hospitals are great places to be if you are really sick but not so great if you are well. There are many sick people in the hospital, some of them contagious. The bacteria in the hospital tend to be antibiotic resistant so if you catch something in the hospital it can be more difficult to treat. You loose your autonomy in the hospital, you require permission to do many things we take for granted at home. There is the unlikely potential for errors to be made that can affect your health. For these reasons I recommend limiting your stay to the shortest time necessary.
Unless your baby needs to be in the hospital longer, I recommend going home after 1 night if you deliver vaginally and after 2-3 nights if you deliver by c-section.