I want to run a django app on a hand-held device. It’ll need to run Python (obviously) and will write its data to an SQLite database.
Are there any tablets available that will let me do this? Specifically, if I bought an Android tablet, would I have to/be able to install linux instead, or would I be able to run it under Android?
If you want Linux probably Meego is the best choice. There is no hardware for it yet, I believe, but there is hardware for the predecessor Maemo.
Running Django on Android is not possible, AFAIK. If you have a network connection the Django server yould be anywhere and you would just need a smartphone/tablet with a browser. That would be the easiest solution.