If speed is not your object, FATE grinding in areas appropriate to your item level is probably the best way to go, as you'll have that small chance of getting an Alexandrite while you're working. Don't rely on it, but think of it as a nice surprise if it happens.

If you want speed, Crystal Tower is an excellent place to spiritbind(if you have a good group), and I hear that Turn 3 of Coil is also beautiful.

On other notes, make sure to have Spiritbind Potions handy, the Spiritbinding FC buff if you can, and Spiritbind Speed increasing gear anywhere you're willing to sacrifice a slot for.