Mt. Olympus (9,030 ft) is the prominent peak above Murray/Millcreek, Utah and is recognizable from anywhere in the SLC valley due to its two long, rocky spines on the West face.
Cascade Springs is a large artesian spring with naturally-terraced cascades and pools, located in American Fork Canyon. Over 7 million gallons of water flow through the springs each day. Cascade Springs isn't a hike, but more of a really easy, casual stroll.
Heugh's Canyon to Olympus Cove (a.k.a. "Z Trail") follows one of the newest sections of the Bonneville Shoreline Trail (BST). It's a 5 mile point-to-point trail great for dogs and trail runs. There are a few sections with sheer drop offs, and for that reason, I don't recommend little kids.
Grove Creek Canyon is located to the east of Pleasant Grove, Utah. It leads you through a somewhat narrow canyon, that eventually connects with the Great Western Trail. Along the way you'll have an amazing view of South Mt. Timpanogos, and pass two waterfalls - the first which is inaccessible, and the 2nd you could probably find a way down to yet wouldn't be easy.
The Tibble Fork Loop Trail (trail #041 & #040) is located in American Fork Canyon, and starts at the Tibble Fork Reservoir, hence the appropriate name. This hike can be done year round, but I find it to be the prettiest during Winter when the trees are laden with snow, the reservoir is frozen over, and the trail offers a certain quietness. The trail steadily gains elevation for the first 2 miles, cuts through an amazing aspen grove and open meadow, then connects back to the Tibble Fork stream and main parking lot.
The Horse Flat Trail in American Fork Canyon starts from the Summit Trailhead, and passes through several meadows, large Aspen groves, and shaded areas before finally reaching the Primrose Overlook.
Lambs Canyon is located off I-80 after passing through Parley's Canyon, but before you reach Jeremy Ranch. Lambs Canyon is part of the county Watershed, and therefore, dogs are not allowed. There are multiple signs saying no dogs, and there was even a county sheriff patrolling the area as well, so don't even attempt to bring them up here. It's a bummer to leave dogs at home, but every once in awhile I want to do a hike that Charlie can't.