Closed Reduction with ENT and then Rhinoplasty later? Or leave broken nose as is and have procedures done together?

I don't like the idea of making fine, definitive cosmetic-rhinoplasty changes right after a nasal fracture. The nose is swollen, the tissues have lots of dilated blood vessels, and you can't do the fine work to get the nose right where you want it.
So in general, I tell my patients to wait about 6-8 weeks and then have the fracture corrected and the real rhinoplasty done at the same time.
You don't *have* to do anything at all to a fractured nose. There is nothing magical that the surgeon does to "fix" a fractured nose. Lots of people have nasal fractures that are never treated.
The only point of having an operation soon after a fracture is to straighten the nose if it looks horribly crooked on the face. Then, it's fine, or even important. If the nose is just swollen, or just a small amount crooked and you're anticipating a real rhinoplasty later, then doing surgery soon can just complicate the rhinoplasty for no benefit.
So when I do an operation within a week of a fracture, I definitely don't try to make any cosmetic changes, and I try very hard not to make any incisions at all. All I do is get the person asleep, and push the bones back into the middle. And I'm done. Really, it's just what the high school wrestling coach does: the kid stands up from a hard fall, his nose is broken and very crooked, the coach puts his thumb on the kid's nose and pushes it back to the middle. Anything else complicates later surgery for (probably) no good reason.
I usually make computer morphs when I'm answering a RealSelf question, to show the changes that are possible for your nose with a rhinoplasty. For example see this page:FacialSurgery.com/RealSelf/RealSelf_Morphs.html
But of course you didn't submit photos for an opinion about the rhinoplasty. See the "Web reference" link, just below my post. At the *very* bottom of the Web reference page is a link to instructions on taking photos that are comprehensive and useful for online consultations like this, in case you'd like a more complete evaluation.

In our experience for over 25 years, closed reduction does not give good results. We perform an open reduction with placement osteotomies in the nasal bones to reduce a nasal fracture that's been displaced. All of this can be performed through a closed rhinoplasty approach with all of the incisions placed on the inside of the nose. It's best only have one nasal surgery, not two, and find the right surgeon who can address both functional, broken and cosmetic issues with your nose. Look for a very experienced, double board certified  ENT/facial plastic surgeon for best results

It is best to perform closed reduction now and wait several months.  Once the broken nasal bones heal out of place, it can be more difficult to correct with a rhinoplasty later.  Therefore, it is important to realign things now.  Usually you have about 2 weeks to perform the closed reduction.  After 2 weeks it becomes more difficult.