Hi, Crafty....welcome to BoneSmart. I'll second everything said above. You will probably be okay to come home directly from the hospital, but if it seems more comfortable to you, you can ask your doctor to approve some time in a rehab facility.
If you're medical expenses are covered under Medicare, there are some specific rules for where you can go. You might do some checking on that now so you will be prepared to tell the hospital social worker where you prefer to be.
Some "rehab" centers are little more than glorified nursing homes and, if you are an active person normally, you might not be as comfortable there. Rehab centers that accept Medicare patients usually have a Medicare wing that is fairly small, so sometimes it's difficult to find a bed. But that's something the hospital social worker will help you with should you decide to go.
The best thing I can suggest is that you do some checking and start talking about it as soon as possible with your medical team.