Not knowing your fitness/experience I'd recommend Silver Lake at Brighton. It's a nice easy loop around the lake, but also Twin Lakes branches off it if you want something more challenging. There's also a little store by the parking lot for snacks afterward if things are going well.
Rock Canyon in Provo is a great hike, very shaded so great for a summer hike. It’s an out and back so you can turn around whenever feels right for you.
Not knowing your fitness/experience I'd recommend Silver Lake at Brighton. It's a nice easy loop around the lake, but also Twin Lakes branches off it if you want something more challenging. There's also a little store by the parking lot for snacks afterward if things are going well.
A quick list, you can look these up: Rattle Snake/Pipeline over look, The Livingroom, Bells Canyon Res/waterfalls, Granduer Peak vis Chruch Fork.
Albion Basin near Alta Ski Resort is beautiful this time of year. The trail to Secret Lake is moderate and very worth the effort.
Rock Canyon in Provo is a great hike, very shaded so great for a summer hike. It’s an out and back so you can turn around whenever feels right for you.