For me, it's tough to say what value a smartphone would have if it could not leverage its hardware aside from being a form of a kiosk. Not harshing you or anything, I just can't see it.
I'd set it up as a behavioral mirror. Naturally I have a horse in this race :)
Inputs would be the actions you take in life (choices you've made) and how they relate to your goals (which depend on actions). Output would be an interactive visualization of past actions. The purpose would be to help improve the quality of your choices (actions you take) to better achieve your goals. Algorithms would work with the accumulated information to pull out correlations, patterns, and in general accelerate the process.
No Internet required, and so much greater security, privacy, and trust than usual. Which is freeing in many ways.
@s73v3r, Self-knowledge can be tremendously rewarding too.
Smartphones aren't going anywhere, but their value proposition is not the only one available. If we were to jump-start our creativity through tight constraints like the X-prize idea, I expect that we'd end up combining the best of our current technology with the best of the new. Or maybe the worst of both...
One of the biggest values I get from a smartphone, and I suspect the vast majority of otherse are with me, is the fact that it connects me to the global repository of human knowledge. Cutting off the internet would neuter it to me.
I'm up for learning though :-).