When picking a lens, you need to consider what it is you want to shoot with that lens. For street/travel, most folks would probably opt for an ultrawide zoom (if they're interested in cityscapes/landscapes or shooting in smaller spaces), a superzoom (for versatility), and/or a few wide-to-normal fast primes (street, night, and across-the-table shooting).
You already have the superzoom. You say you don't want the ultrawide (EF-S 10-22 or Tokina 11-16/2.8 are probably your best choices there), so maybe all that's left to contemplate are the wide-to-normal primes.
However. You may also want to keep in mind the fact that travel is when you're most likely to get gear stolen/broken/lost. It's also when you may want to keep the bag lighter than you would back home, when you can stash things in the car. Going for small, cheap gear might be better than looking at L lenses, unless you've got great insurance, or are traveling solely for the purpose of photography.
The two candidates I'd propose would be the EF 35mm f/2 IS USM (if you want to spend a bundle), or the EF 40mm f/2.8 STM or EF-S 24mm f/2.8 STM if you don't. Both EF lenses are closer to normal on a crop body camera like the 60D than a 50mm would be; the 24/2.8 is a 35mm full-frame equivalent. And all of them are sufficiently fast for available light shooting--the one thing your 18-135 can't handle. Were you planning on shooting indoors without a flash at any point? In addition, the 40/2.8 is not only low-cost, and sharper than the EF 50/1.8 II @f/2.8, it is a pancake lens (as is the 24/2.8 STM). Super-compact, and very discreet for street shooting.
But these are what would work for me. You are not me. What would work for you could be completely different. Consider analyzing the images you like that you've taken with your 18-135 and seeing if there are any focal lengths you tend to use more frequently. EXIF analyzing tools like ExposurePlot, or Lightroom ability to show images by metadata might help make it clearer if you have a "missing" focal length, or one that you favor.
You may also want to consider renting lenses for the trip, rather than purchasing them, if the lens isn't one that you can see yourself using when you get back home. So, you could have an ultrawide available for the trip and if you decide it's not your cup of tea, the rental will have cost far less, and you get to send the lens back.