I have the Canon 10-22mm which I really like but don't use that often. There's also a 15-85 if you were wanting to cover that focal range. I'm afraid I don't know much about Tamron and Sigma.
I LOVED my Tokina 11-16mm. As with any ultra-wide lens, there is distortion, but it's not bad and easily corrected. You are only going to notice it if you are shooting a brick wall or something with obviously straight lines. I, personally, like the distortion and often use it to my advantage. I just got a full frame camera, so I sold my 11-16mm. I sold it for $375, I think. So if you can pick one up used, you are getting a great bargain. It is a solid, high-quality lens. Much better built than all of my crop-sensor Nikon lenses I owned.
I have rented the 10-20 f/3.5 DC Sigma (for an APS-C cropped frame). A nice, resonably fast, constant aperture lens, I had great results with my Nikon D5100. There are mounts for many other manufacturers. If you have a full frame camera, consider the 12-24 DG Sigma which has a sterling reputation although I have no experience with it.
Distortion was imperceptible. I don't remember correcting any of the shots I took. Straight lines are straight even at the edges of the frame. I did try the Tokina 11-16 for a day, but liked the extra length of the Sigma. It is extremely versatile and it's that top end up to 20mm that decided me on this rather than the Tokina.
For "close" shots, the 10mm end the wide angle handles things beautifully, gobbling up everything in the wide angle. The "juror's door" image below was shot on the top step with the front foreground only inches from my feet. The bridge picture was shot almost touching the front stone work.
Most reasonably priced. This will probably be my next lens purchase. Here are a few images with this lens and my Nikon.
I have a 10-22 canon and I really really like it. There is some distortion at 10 but I like to use that for some shots that I'm getting. I don't have many examples on here but this one was taken with that lens. I was basically touching the tank wheels with the lens in this shot and as you can see there is some distortion but it actually kind of works for this angle and shot in my opinion.
I have the Canon 17-40 f4 L series, which on a cropped sensor gives you about 27 - 65. Perhaps not as wide as you were looking for, but it's a great lens, stays on my camera pretty much all the time, gives a lot of flexibility. See this for focal length 27mm:
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Distortion was imperceptible. I don't remember correcting any of the shots I took. Straight lines are straight even at the edges of the frame. I did try the Tokina 11-16 for a day, but liked the extra length of the Sigma. It is extremely versatile and it's that top end up to 20mm that decided me on this rather than the Tokina.
For "close" shots, the 10mm end the wide angle handles things beautifully, gobbling up everything in the wide angle. The "juror's door" image below was shot on the top step with the front foreground only inches from my feet. The bridge picture was shot almost touching the front stone work.
Most reasonably priced. This will probably be my next lens purchase. Here are a few images with this lens and my Nikon.
http://365project.org/frankhymus/iphone/2013-03-20
http://365project.org/frankhymus/iphone/2013-03-17
http://365project.org/frankhymus/365/2013-03-17
http://365project.org/frankhymus/work-in-progres/2013-03-19
I agree with @cmc1200