What do you do if you are Braxton Miller?  He has graduated so he can transfer as a graduate student and play immediately next year. There is a story out now about him having interest in possibly transferring to FSU, Oregon, Ole Miss, and Duke (weird collection of schools), though Urban Meyer has said he expects him back at OSU and that he hasn't made any inquiries about transferring.  So if you are Braxton Miller, what do you do?

Go to the school that will improve my draft position the most.    And, odd as it sounds, that's Duke.    Weak ACC schedule and Cutcliffe is looked at as some QB-whisperer. 

Go to FSU, get compared to Winston.
Go to Oregon, get compared to Mariota and be forced to play in a tougher PAC12.
Go to Ole Miss and play the SEC West schedule.

Duke.

I left out "return to OSU" as an option.

Barrett played too well.    Miller "wins" the starting job in the spring, struggles for a game or two, gets the quick hook.    The ONLY reason to return to college is to improve your draft stock and you can't do that if you're involved in a QB controversy all year.

Is he a QB draft prospect?

Leaving is a no brainer. Looking at schools, #1 is making sure there's a clear path to the starting job. If Oregon or FSU have that, that's the place to go.

Depends on which scouting report you read and his willingness to swap positions.   I've read "late round QB project" more than once.

If he doesn't want to swap positions, it's Duke.    The coach and the schedule will allow him to showcase his suspect passing skills better.  
If he's down for swapping positions, there's no reason to return to college as a QB. 

If he is going to switch positions, I see no reason for him to leave OSU.  He knows the system, knows the coaches, knows his teammates, etc.  That will make it much easier to learn a new position. 

Yeah, I meant to add that.  Meyer has a lot of respect from NFL coaches.   A good word from him will at least get you a tryout at the next level.

Duke's schedule isn't the only reason why Braxton would go there. People don't realize it but they have talent all over that offense now. That and Cutcliffe is just a ridiculous coach. 

A lot of talk that Cardale Jones might declare for the draft.  I wonder if that changes things for OSU and Braxton Miller if he does.

That would prove CJ is a dumbass.   Of course, if he doesn't care for school, and I doubt he does, being drafted in the 6th round might be better than going to Basketweaving 101 for the rest of the school year. 

I don't think he is a 6th round pick, I think he goes in the 3rd or higher, which might be the highest he will go if he goes back to being a backup

I was being pretty generous with 6th round, I think.     He has a resume' of three games.   There are 3-4 year starters that aren't even on a practice squad.    If you want to say "He's 6'5", 250 with cannon", I'm not going to disagree.    But he started the season as a 3rd stringer and only got to play because of two injuries.   What did Urban Meyer miss?

Meyer didn't miss anything. You however missed the fact that the two guys playing in front of Jones were both legit candidates to win the Heisman at one point in the season. Lots of successful NFL QBs found themselves sitting a college bench for a while behind much less talented guys than those at Ohio State.

Pretty sure I'm aware of who he was sitting behind.   Want to name the 3rd string college QBs who only got to play due to injury, played 3 games, declared for the draft and went on to successful NFL careers?

And weren't you the ******** who tried to compare Ryan Lindley to Cardale Jones?  3rd string to 3rd string?

He has a short, but compelling, resume coupled with all the physical tools scouts drool over.  And it's not necessarily about what Meyer missed - he's picking the guy who he thinks will win him the most games at OSU, not who will make the best pro.  Those aren't necessarily the same thing.  I think you can find where people were saying Jones was the best pro prospect on the roster even before he got playing time.  It does seem sort of ridiculous, but you definitely are seeing the idea that he's a 3rd round type out there at this point.  I'll be interested to see if that holds up once we get away from the moment and he starts to come under more scrutiny, but he doesn't get the benefit of waiting to see that before he makes the decision.

IF he would be a 3rd round pick, since he can't transfer and play right away and has no assurances of getting the job at OSU, going pro might be his best option.