The most important thing is to realize that the famous waterfalls are highly seasonal, and many of them are dry or just a trickle by this point in the year. Most of the pictures and videos you see of the waterfalls were taken in the spring when they are at torrent levels. Towards the end of summer they are much reduced in volume and some of them are bone dry. The monstrous Yosemite Falls will probably be just a gossamer spray, if anything. The three waterfalls in the Yosemite Valley are that are most likely to be still running are Bridalveil, Vernal and Nevada falls, although none will be at their maximum flow. If you keep that in mind then you won't be as disappointed as many tourists are who go there in the late summer and fall. The park is still extraordinarily beautiful and spectacular even without the waterfalls.
Yosemite is a gigantic park, almost 1200 square miles, and there is so much to see and do there that you can't possibly see it all in one trip. You will have to choose which things interest you the most. Fortunately you are going there at a time when virtually the entire park is open and available. In the late fall, winter and early spring, Tioga Road and Glacier Point road are closed due to snow, but they are both open at this time. You don't say how many days you are going to be there, but I would recommend that you divide your time between Yosemite Valley, the northern, upper park along Tioga Road and Tuolumne Meadows, and the southern part of the park including Glacier Point road, Wawona and Mariposa Grove. Your admission fee of $20 per car is good for 7 days of admission, so keep your receipt. There may still be a chance of encountering mosquitoes, so bring a good mosquito repellent such as Cutter Lemon Eucalyptus, sold at Target. Sunlight and UV rays are very strong at the higher elevations so if you plan to do any hiking bring lots of sunscreen. Stock up well on water and food snacks that you can carry with you. Prepare for either hot or cold weather, even though extreme cold is very unlikely at this time. At the higher elevations the nights can get pretty chilly even if the day was hot.
In Yosemite Valley, some of the best sights to see include Tunnel View (now called Yosemite Valley Overlook), Bridalveil Fall, Fern Spring (which is just south of the Pohono Bridge on Northside Drive), Valley View on Northside Drive, El Capitan Meadow, Swinging Bridge (the current bridge there does not swing), Lower Yosemite Fall (the trail winds through a beautiful area even if the fall is dry), the free 30-minute movie at the Visitor Center, the Mist Trail to Vernal and Nevada falls (and further to Half Dome), and one of the best spots in the entire park in my opinion, Happy Isles. Most people pass right by Happy Isles in their relentless pursuit of the Mist Trail and Half Dome. Yet I think the stroll around the Happy Isles (3 islands in the Merced River) is one of the best places, with water rushing everywhere around you in the springtime. It's shady and cool and refreshing. Mirror Lake is a popular destination (1-mile hike) but it is very crowded with lots of kids splashing in the water and has the atmosphere of a playground more than a national park. If you want quiet, don't go there, and stay away from Curry Village with the huge crowds. You can take free shuttle buses around the valley and that will save you a great deal of worry about where to park over and over again.
Along Tioga Road, there are many sights to see including Tuolumne Grove of giant sequoias, (which requires a 1-mile walk from the parking lot to the grove, and the walk back is uphill), Siesta Lake, White Wolf campground which is the staring point for some hikes in the northern park, Yosemite Creek, Olmstead Point with a great view of the back of Half Dome and interesting glacial erratics, Tenaya Lake and the climbers on the Stately Pleasure Dome next to it, the Cathedral Peak area (there is a hike from Tioga Road up to the small waterfall coming off of Lower Cathedral Lake) and Tuolumne Meadows, which is the largest subalpine meadow in the Sierra Nevada mountains. It is the staring point for many hikes, short and long, easy and hard. You will have to study the list of hikes starting from that area to decide which interest you. Tioga Road continues to the park's east entrance and then to the spectacular Ellery Lake outside the park, then down a steep and scary grade to Lee Vining.
Hetch Hetchy is another area in the northern part of the park, not on Tioga Road, which is less visited than other areas. It once was a beautiful valley almost considered a twin of Yosemite Valley, but it was dammed (over the protests of John Muir and conservationists) and a lake was formed, Hetch Hetchy reservoir, which supplies drinking water to San Francisco. San Francisco residents who pride themselves on their supposed environmental credentials hypocritically oppose the removal of the dam and the restoration of the Hetch Hetchy valley to its natural state. You can visit that area and take hikes there, but that area is known for having a lot of rattlesnakes.
Glacier Point Road is south of Yosemite Valley and leads to the famous Glacier Point, arguably the world's best viewpoint that can be driven to, rivaled only by points along the rim of the Grand Canyon. Washburn Point is just a half-mile to the east also along Glacier Point road. The best time of day to visit Glacier Point is sunset, when the orange alpenglow bathes Half Dome and the mountain peaks of the park while the valley 3,000 feet below fades into deep indigo. But it is still a great view at any time of day. Back down from Glacier Point, along the Glacier Point road, is the parking lot for Sentinel Dome and Taft Point. Only go to Taft Point if you enjoy being terrified by 3,000-foot dropoffs with almost no guardrails anywhere. However, Sentinel Dome is an outstanding alternative to the grueling and dangerous Half Dome hike. Sentinel Dome is only 2.2 miles round trip with an elevation gain/loss of only 300 feet (compared to Half Dome, minimum 14 miles round trip and an elevation gain/loss of 4,700 feet). Yet Sentinel Dome gives you the same panoramic views of the park and the "being on top of the world" feeling that Half Dome does, with much less time and effort and danger involved in getting there. Sentinel Dome is also a great spot for stargazing at night, due to its elevation (8,122 feet) and unobstructed 360-degree view. However it will be chilly up there even if the day was hot. So if you go up there for stargazing, bring a blanket and pillow, and a flashlight for the walk back in the dark.
The southern part of the park includes Wawona, a historical area which has a large, 100-year-old hotel, with a small golf course (the only golf course within a national park, as far as I know) and the south fork of the Merced River. It seems more like a mountain resort than a national park. At the park's southern tip is the Mariposa Grove of Giant Sequoias, the largest sequoia grove in the park but also the most popular and crowded. There is a free shuttle bus from the Wawona hotel to the grove, which guarantees you admittance to the grove even if the grove's parking lot is full. There are an upper and a lower grove of sequoia trees, and tram ride (for a fee) that takes you through them, or you can just walk. Some people take the tram to the upper grove, then walk back down. The largest tree is the Grizzly Giant. There are other groves in the park which are less crowded, such as the Tuolumne Grove and the Merced Grove. Those provide more of a quiet, deep-forest experience than the Mariposa Grove does.
Plan for every meal to be a picnic lunch or a picnic dinner somewhere, even the first day you get there go into a grove with some sandwiches and eat there, and let the immense silence of the forest replace the sounds of the freeways and cars. The silence will seem profound and all you will hear is the sounds of nature. In the late afternoon and at dusk deer will stroll by nonchalantly. Don't leave any food and don't have any food in your car after dark because bears will break into your car to get it, causing considerable damage. Only bring the food that you know you will eat. There are a couple of small stores to buy food in the park, at Yosemite Village in Yosemite Valley, Tuolumne Meadows, and the gas stations at Wawona and Crane Flat. But the selection is limited. Buy the majority of your food before you go into the park and then only buy what is needed when you are there. Gasoline is sold at only 3 locations in the park: Wawona, Crane Flat and Tuolumne Meadows. The price is 50 cents higher per gallon than outside the park, although I think it is well worth the convenience and time saved. Gas is not sold in Yosemite Valley.
When you enter the park you will be given a map, a newspaper called "Yosemite Guide" which lists events, times and locations, and a full-color booklet that is a guide to the park. If you don't get all 3 of these, ask for whichever one you didn't get. Sometimes they don't give the color booklet but they almost always give the map and newspaper.
The most important thing in my opinion is to sit still somewhere in the park and just take it all in. So many people go to Yosemite with a laundry list of things to do and things they want to see, and rush around from place to place, checking off things. They may succeed in completing their list, but I think they never achieve the gestalt of the park, the feeling of actually "being there" and being part of it. They only get the experience of having passed through it and seen the famous sights. Pick a spot that appeals to you, whether it's a spectacular view, or a babbling creek in a forest, or anywhere, and just sit still for a while and take it all in. This is the way to truly experience Yosemite and many people fail to do this at all during their time there. So don't try to pack every day with activity after activity, hike after hike... just leave some "down time" where you can just relax and "groove" on it. In spite of that, it is also good to study the park beforehand and decide on which things you want to do while you are there. Web sites that can help you with this include these:
http://nps.gov/yosehttp://yosemitefun.comhttp://yosemitehikes.com