I guess this is the beginning. I've been working on the software side of things first. Right now, it is based on headtrackr https://github.com/auduno/headtrackr/ which uses three.js http://threejs.org/
I'm currently using a TARDIS interior model from Adam Bullock http://daleks.adambullock.com/models/models.html I'm not sure if I'll find a better one, or just modify this one to suit my needs.
I'm still working on what will ultimately be used for hardware to display the TARDIS interior. Since the software is web-based, it can run on any number of devices. If I can get it to run on a tablet, that would be easiest, especially with an integrated camera. My other thought was to repurpose an old laptop.