I have to go to Nebraska and dig up peony bushes this weekend 11/8/14 and bring them back to Illinois. Can I still plant when we get back? Or how do I store them? They are my grandfathers plants that he planted for my grandmother and we really want to keep them. They will be destroyed soon.

Assuming the soil won't be frozen when you get back, you would still be able to plant them. It's getting extremely late to do so, since the recommended time for dividing/replanting them is early fall so they can get their roots established. Getting them in the ground would be safer than trying to place them in cold storage. I would be sure and cover them with a light mulch to give some extra protection for the winter. As peonies don't like to be moved, you may have a 1 or 2 year wait til they bloom again. Also, be sure the crown (eyes) are not more than a couple inches below the surface of the soil.

Yes, they can be dug up and transplanted. When being planted, be sure not to plant them too deep as this will delay flowering. I would expect them to be dormant when you dig them up so note how far down in the soil the tubers, buds, eyes are and match that here. You could also mulch them in with straw to delay the soil temperatures from freezing and allow establishment to begin/continue into colder weather. Be sure you water them well when you do plant them to settle the soil.