The EF-S 15-85 IS USM is the best Optical APS-C zoom from Canon. For image quality it is the best!
But it is a pretty slow lens for the amount of money, The 17-55mm F2.8 is an alternative but you loose even more in the tele end. In the Canon world the 15-85 is optically better than the 17-55mm and in the Nikon world it is the 16-80 that you should stay away from and get the 17-55mm.
The 18-135mm V1 is just a regular kit lens.
The 18-135mm Nano USM is optically no better than the 15-85mm , but its AF and IS is prob the best.
Your 15-85mm is a good option but keep in mind it is far from perfect for indoor and lower light. That is were you probably want to use a speed light. If not, than stay away from this lens. (PS this lens get listed on eBay rather frequent and you are prob better of buying used.)
It all depends on you, and how much you obsess over your images. I have never had the 18-135, but have had the 17-55 and two 15-85's.
I use the 15-85 for a every day outside lens, as well as in my studio where I have adequate lighting. I bought my 2nd 15-85 after getting a SL2 as a second body, I recommend it as a very good lens, but its not a match for my L lenses. The focal range of the zoom is excellent, the 15mm wide angle is very useful.
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.