What I am about to say is going to sound a little contradictory, but bear with me. If your primary usage is video, the t3i may be your best option among the 3. The 7d is a superior camera in terms of build quality and when it comes to still photography. The t3i is pretty much the t2i with an articulated screen and a couple of minor features. if the articulated screen is not that important to you and you can get a significant discount on t2i compared to t3i, that is not a bad choice since you can apply the savings to a better lense. In my personal experience, the articulated screen is worth about a $100 difference. There is NO difference in video quality between t3i and t2i. On the surface, there is no difference between the video quality of any of them since they use the same chip. In real word practice, the 7d might (and i really stress might) wield slightly better results due to features that are more geared towards helping the professional like being able to dial in color temperature. The 7d also yields slightly better results in high iso shots.
The t2i and t3i do have one advantage over the 7d and that is the ability to use the magic lantern hack. This 3rd party firmware provides extra functionality like focus assist and the ability to disable the AGC for sound.
I personally own a 60D and shoot with a t2i w/ magic lantern at work. I enjoy both although once i got the 60d, the t2i felt even more lightweight and fragile than I noticed previously. For me the 60d was a good compromise of the extra features of the 7d while being closer to price to the t2/3i range. I also figure canon will be replacing/upgrading both the 5d and 7d in the near future so rather than spend money on 7d now, i will get the most out of 60d and maybe upgrade when new versions of 7d or 5d are available.