Something that should be mentioned for a first timer is the altitude in parts of the Park. If you are only going to be in the Sierra for a few days, you should be aware that much of the high country is above 10,000 feet elevation above sea level. Yosemite Valley is easy to adjust to, being around 4,000 feet, but the trail-heads along the Tioga Pass Road start at over 8,000 and go up. Likewise, the Yosemite Falls trail starts on the Valley floor and goes up over 2,700 feet if you go all the way to the top. The hike from the Valley floor to Glacier Point is less than 5 miles but gains 3,200 feet, making it a real grunt.
Folks who have little experience with higher altitude hiking can be surprised if all they look at is the distance on a map. Steepness and altitude can make what appears to be an easy walk into something else entirely. Mt. Dana is a case in point. I've been up there, as have most old Sierra hands. It is beautiful and a rewarding climb. It also tops out at over 13,000 feet, which is serious altitude for someone who hasn't done that before or has just driven up from sea level.
The above is not to discourage anyone from enjoying the wonderful back country of Yosemite - as well as our other parks like Sequoia and Kings Canyon just to the south. It is just a word to the wise that high altitude hiking should be taken seriously and prepared for. Fitness is important but so is a little acclimation. Visit the Park and surrounding areas, get used to the moderate elevation gain from SFO or LAX to Yosemite. Spend a day or two at 4,000 feet, then one at 8,000, then after a few days go ahead and try Mt. Dana or some of the bigger domes above Tuolumne Meadows. It'll be more fun with a little acclimatization.