Tokina 11-16 is really a great lens, and one I wish I had - not for landscape work, but street shooting. The f/2.8 is a great tool to work with, but not particularly advantageous for landscapes unless you're shooting under low light. It's also around $700, which takes it out of the budget lens/bang for your buck category for most new shooters. My 12-24 f/4 Tokina has served me very well over the years, and even been put back together twice by Tokina Service in Huntington Beach CA. Street price is around $400 - and the extra range may wind up being more useful. I usually shoot in environments where I'm working in low light (theatre, street, reportage etc) where I need a fast lens/shallow DOF, and a f/4 lens doesn't work as well. The last time I used the 11-16 was on a FF body (5D mkiii) shooting in the middle of the night in the Tenderloin, San Francisco. It worked brilliantly, once you accepted the vignetting on the full frame sensor. But, I'm getting off track from the OP's question.
It's worth remembering that quality lenses hold their value remarkably well. If you buy a decent lens and don't abuse the heck outta it, you should be able to resell it quite easily if it doesn't work out for you. On
POTN it's not uncommon for see stuff sold within a day of being posted. Tokina makes very solid lenses, and if I remember correctly, was started by Nikon/Nikkor folks. Canon 10-22 is quite popular, but it's around the same price as the 11-16 Tokina. Sigma 10-20 is under $500.
Personally I'd recommend either Canon 17-40L . You can pick up a used one under $500. Or the
15-85 IS, rather then going all the way into UWA territory.
Good option is renting a lens you are interested in for a week, and seeing how you like it. There are some great rental companies out there, but my vote goes to Borrowlenses.com. The 15-85 is $41 for a week.