Hollow's Last Hope is free, short, and has options available for expanding on it later(Crown of the Kobold King, Revenge of the Kobold King(free), and Hungry are the Dead turn it into a mini-AP that caps at around level 8.) However, it's going to need some conversion from 3.5 to PF. That's not all that hard though. Starts at level 1.
Dawn of the Scarlet Sun is free, short, and starts at level 5. It's meant to be played with 6 players, rather than the more typical 4. I think it was originally meant to showcase the classes from the APG.
We Be Goblins! and We Be Goblins Too! are both free and short, but I'm pretty sure they're meant to be run only with the 4 pre-generated characters. We Be Goblins starts at level 1, while We Be Goblins Too! starts at level 3. They can be played in succession from what I understand.
Master of the Fallen Fortress is also free and short. Starts at level 1.
All of these were Paizo's contributions to Free RPG Day at some point. I've personally only played Hollow's Last Hope, and am in a game where it seems to be expanding into a modified Crown of the Kobold King/Hungry Are the Dead. I give it a thumbs up as a good module.
There's also a bunch of old 3.5 modules that are part of the Great Golem Sale right now for super cheap, and some PFRPG modules, at a slightly higher price, as well. Print versions only, however. I think any of them would be good starting points, and they run the gamut of types and recommended levels. I think one of them even starts at level 16 or so.
Really, any single module will make for a short game, as they're not usually meant to run longer than 3-4 IRL table sessions from my experience.
