I did this also. Switched from a best of breed Android phone, to a Blackberry.

Yes. A Blackberry. One of newer ones that runs BB10. It supports just enough to enable me to read mail, and message my friends, but there are hardly any useful apps for it, and most of the Android apps that you try to install on it barely work either.

Added bonus - The built in Facebook app no longer works either.

End result, the Blackberry sits in my pocket 99% of the time. My phone is now a tool again, and not a distraction.

It's perfect for me - but your mileage may vary, of course.

Edit: like Fratlas, I also get about 2-3 days of usage out of one charge.

It's an iPhone 4 with a broken mic which I got for free. It's too old to run a lot of distracting apps (VSCO, Snapchat etc) and I can't call people. I have a $20/month (AUD) prepaid plan for 1GB data which gets me through easily. I guess it can only figuratively run maps/camera, but it's enough to keep me from using it 24/7. Battery also lasts several days because I use it so little.