We did the parks without cell phone in Oct 2015.
We are Canadian, and didn't want to pay extra for a data plan in the US. But also, we made a commitment to look around us and not at our phones, and we pledged to leave our phones in the hotel safe.
We had a day-planner thing from the Birnbaum's guide that we ripped out, it had our dining reservations and fastpass times on it. We learned where the kiosks were to change or get new fastpasses.
I think unless you are the type of people who change plans a lot at last minute, you can easily do the parks without any device at all. We made some dining reservation changes a couple days ahead from the wifi in our room.
There are too many phone-staring zombies in the parks already! I figure I'm spending all this money, might as well enjoy the people-watching, interactions with Cast Members and guests, details in the theme park itself - things I would miss if I had a device and was wriggling a wifi signal out of it to check times on anything.