Use sunset as your turnaround alarm.
Two trails reach this summit and they join just west of Emerald Lake, so your choice is really about the approach. Timpooneke works up through open meadows and a run of small waterfalls, with Scout Falls and its overlook about a mile and a half in, then 2.2 miles of switchbacks from the lake to the summit house. The Forest Service calls this possibly the most used trail on the whole forest, and Saturdays are the worst of it. Snow holds on up high into midsummer.
Utah's most beloved summit: wildflower basins, a glacier remnant, mountain goats, 11,752 ft.
3+ liters water, broken-in boots, layers for weather swings, headlamp, real food (jerky, trail mix), trekking poles, first-aid kit, and an early start.
Make it a weekend: Timpooneke Campground (Camping, 0 mi) · Mount Timpanogos Campground (Aspen Grove) (Camping, 3 mi) · Granite Flat Campground (Camping, 4 mi) · Manila Creek Pond (Fishing, 4 mi)
More hikes nearby: Stewart Falls (Hike, 3 mi) · Battle Creek Falls (Hike, 5 mi) · Bridal Veil Falls (Hike, 7 mi) · Cecret Lake (Hike, 10 mi)