The hiking in Yosemite is world-class, and it is perfect in June, as most of the trails have opened and the weather is near-perfect. The park has over 800 miles of hiking trails, and many lead to waterfalls, alpine lakes or granite peaks. Trails vary in distance and difficulty, so there is something for all ages and levels of experience. You can read about the best hiking trails in Yosemite, and NPS’ list of trails here.
Remember, when hiking in Yosemite, bring plenty of water. It is recommended to bring at least 3-liters water for a day hike. Also, stick to the trail; going off-trail can lead to erosion, as well as injury. And, if hiking to a waterfall, never swim in a pool above the falls.