It sounds like you want to day hike the Valley so this is day hike advise not backpacking advise.
First of all come out in late spring, early summer not july or August, less people and more water. In August it can get to be 100 degrees in the Valley and the waterfalls have mostly shut off to a trickle.
1) hike from glacier point down the Panorama trail past illouette to Nevada falls and down to Happy Isles. The shuttle bus will drop you off at glacier point. Expect alot of people at the bottom but it's still the best hike in the valley.
2) Walk the valley floor, few people do this these days but it's a rewarding loop. Take the shuttle to Bridal Veil and then hike the old wagon trail towards Curry Village, going up the 4 mile trail which is along the way is strenuous but provides some great views of El Cap or you can get the same views by taking the shuttle to the south rim and visiting Taft Point.
3) Take the shuttle bus to Tuolumne meadows and hike down the Indian Ridge trail to North dome and view Half Dome from the North Rim. Come down the trail at Yosemite falls.
4) Hike around Hetch Hetchy to Ranchiera Falls (June not July or it's too hot). There is a great slide of water there worth seeing.
5) Take a loop around the Redwoods, still snow there in June. If the road has not been plowed skip it.
Also the falls at the bottom of the trail to Chilnualna Falls is one of my favorite places to visit, like a giant Japanese water garden. I'm not recommending the 4 mile hile up to Chilnualna Falls just visiting the falls at the bottom, a short 1/4 mile hike from road about the redwood cabins up the road from Wawona.
You can't go wrong, anywhere you hike it's Yosemite.