I've had all three versions of the 18-135mm (only have the newest Nano USM version now), as well as the 15-85mm and the 17-55mm.
I agree that the 15-85mm is the way to go, if you're after image quality. I like using it at outdoor car shows. That extra 15mm at the wide end can make a difference when things get crowded and it is difficult to back away to fit the subject in the frame. Also, you can't beat USM autofocus.
All of the 18-135mm lenses have been OK. Image quality is good enough, but it never wowed me. That 18-135mm focal length range is so useful, though, and that is why I still own one. I'd recommend going for the STM or Nano USM version if you can. I'm not a fan of focus by wire, but I remember thinking the faster and quieter autofocus was a nice upgrade when I switched from the original 18-135mm to the STM version.
The 17-55mm is fine, but I don't have any great enthusiasm for it. It's not a bad lens, but it has never impressed me. I rarely use it. I find the extra focal length range of the 15-85mm more useful than the f/2.8 of the 17-55mm. But that's just my personal preference. I also find the lens creep of the 17-55mm annoying.