It depends entirely on the award program you use to book the tickets, they are all different.

I would suggest you look at the programs you can convert to from Chase, read up on the airlines you can redeem for from those programs and the miles required, as well as whether they allow stopovers.

If you have reasonably fixed dates you may want to start with looking for award availability first, as its no good converting to the 'best' program if there are no award seats when you want to travel.