Yes after having a skin graft you'll need to stay in the hospital for at least 3 to 4 days for most skin grafts so that the hospital staff can monitor you for any potential complications.
Then if there are no complications from the skin graft surgery then you will be discharged but still should take it easy for a month or so after the skin graft surgery is done.
Some more major skin grafts may mean you need to stay in the hospital for around 2 weeks before you're discharged.
Fully recovery after a skin graft can be a few months to 6 months after the skin graft surgery but some people recover within a month.
It all depends on how severe the skin graft surgery was and the bigger the skin graft the more recovery time and the smaller the skin graft the less the recovery time takes.