I can't chat about dog friendly hikes and not throw a bone to Tanner Park or, specifically, Parley's Nature Trail.
With the endless options of off and on leash trails near SLC it feels a little silly to talk about a crowded, often urine-soaked, dusty trail in the middle of the city but if you can look past these things you have an incredibly accessible puppy playground in your backyard.
The closest parking lot often fills up but there is plenty of street parking. PLEASE please bring your leash for the short walk from the street or lot to the trail. I have been a few times a week for the past month or so and I can tell with all certainty there is no rhyme or reason to when it is most occupied. I have been on a cloudy Tuesday afternoon and had to dodge kids and dogs and steaming piles of leftovers left and right, then on a sunny Saturday morning we had full fledged Mortal Combat (I'm Nightwolf, natch) battles with no interruptions.
Osa & Jasper are always searching for the next spot to get wet, which Parley's delivers on. There are two main access points where you will see a congregation of dogs and the people they own, but we prefer scooting off to the creek immediately after sprinting down the steep and dusty entry to the trail. When the ground levels off take the left at the fork, this will take you around a patch of trees and you will quickly link up with the creek that trickles slowly (in the summer) through the park. Thats our spot, you're welcome to share it with us.
Be advised that there are bike trails that run thru Parley's and we only needed one near miss to decide to avoid that area of the park altogether. Helmet-less folks bombing full speed down concrete tangling with 70lbs of goofy uncoordinated fur is not a combination I want to witness. Stick to the fence line on your right and you'll be safe from the adrenaline junkies on wheels.
If it isn't evident by now I'll come out and say it: I have a bit of a love/hate with this dog park. Convenience and space for high speed chases make it incredibly tempting, but it's heavily trafficked and I've heard rumors of dogs getting ill from other visitors. Plus, at the end of the day if I can spend ten more minutes in a car and get into the mountains it feels a bit 'easy' to stick around the City. So, in summation, for the quick and dirty head to Tanner Park, but on your visit please remember:
"Pup dropped a deuce? Dont leave it loose."