I am not aware of any device like you described that doesn't have internet capabilities. If you are using T-mobile or At&t, you can buy an unbranded/unlocked GSM handset and have the internet blocked but if you buy it from them, you will be required to have a data feature. Keep in mind you can't do the same thing w/ Verizon or Sprint.
I am looking for a phone for my son for his birthday, but I want a phone without internet. I do not want an app or OS on the phone that would support browsing. He would like a touch screen and full keyboard, which I think is going to be hard to get without internet. If I have to get a phone with internet and a no data plan, can I also alter the phone so he does not even see the web app or link on the screen of the phone?