One of my favorite hikes in Park City is Bloods Lake in Guardsmans Pass. It's so beautiful and fun for the whole family. Yes, toddlers and babies too. Our oldest, Luna (age 2.5 at the time) hiked most of the way and daddy carried her the rest while I carried our youngest, Soleil, in our Baby Bjorn.
The hike is about 2.8 miles round trip, and the views are worth it. It's a dog-friendly trail although dogs are not allowed to swim in the water at the top.
It is definitely a very popular trail (for good reason), so I recommend starting early to snag a parking spot and avoid crowds. Also, be sure to bring your mask as you will have to pass by many people on the single-lane trail. We like to step wide off the trail when people are hiking toward us (and remember that those hiking up-hill have the right-of-way).