You will definitely not get a week out of a 9V cell - they have very small capacities (and are expensive relative to other types of cell).
Your Uno already has a regulator in it and this regulator wastes a certain amount of energy converting between different voltages. I'm certainly no expert, but from what I've gleaned over the last month or so of owning an Uno, powering it from batteries can be tricky if you want to do it for long periods of time.
It's probably worth trying a 12v sealed lead acid battery - these have capacities measured in Amp Hours, rather than milli-amp hours like most other types of cell. The built-in voltage regulator in the Uno is good up to 20V, just be sure to connect to the barrel jack on the board.
Of course, without knowing more about what you're actually trying to power along with the Uno, it's difficult to make proper recommendations.
I would also suggest looking at building your system with a naked MCU and a voltage regulator tailored to your application. That way you can throw away a lot of the stuff that uses power on the board that you don't need. (Start with a Breadboarduino and take stuff out from there!)