Agnew lake is one of the many higher elevation lakes found in the June lake area. June lake area itself has wonderful lakes, but if you want a bit more solitude and great views, Agnew lake is a good hike.
The base of Agnew lake is about 2.1 miles from Silver lake or the Rush creek trailhead. https://www.alltrails.com/trail/us/california/rush-creek-trail-to-agnew-lake. However, do not let the distance fool you. You climb the 1,256 feet on the face of the canyon and when the sun is up, it gets hot very quickly. The first mile is far more intense than you anticipate.
If you want an even better view of the lake, do not take the Rush Creek trail, but continue climbing towards Clark lake. A half mile or so, you get the view presented in this photograph. You can see the entire Agnew lake, with Silver lake down below and far in the distance, you get to see Mono lake as well.
You can probably do this hike and back in about 3 hours time, or your can proceed either towards Gem lake or Clarke lake for a longer hike.