You could probably find some AA fare that would allow routing JFK-LAX-MIA-XXX, you would have 12 hours in lie-flat followed by 1-3 hours MIA-XXX.

Seriously, pick the destination and then worry about the flights. The destination and hotel choice have a huge impact, hopefully a week or more of your time will be shaped by those choices. As long as the destination is served by 'big' planes as opposed to RJs or props, the flight won't be long enough to worry about, a few hours.