According to the NPS, if you start the hike at the Happy Isle shuttle stop (#16) the roundtrip to the top of Nevada Fall via the Mist Trail is 5.8 miles with an elevation gain of 2,000 feet. I used the 24K topo map in my GPS and found the numbers to be reasonably close and pretty much confirm the NPS numbers. Allow 5 to 6 hours for the roundtrip. I've done this hike and it really feels like 10 miles because of the steepness of the trail in sections. The stretch of trail up the side of Nevada Fall is a tough one, gaining approximately 700 vertical feet in a half mile or less.
As an alternative you should consider the Panorama Trail starting at Glacier Point and ending at Happy Isle. That trail is 8.5 miles one-way, descends 3,200 feet to the valley floor and takes about 5-6 hours. If you have just one car, leave it parked in the valley and buy a ticket on the hiker's shuttle that leaves Yosemite Lodge at 8:30 and 10:00 in the morning. The ride to Glacier Point will cost you $25 but makes it possible for you to do a one-way hike back into the valley. The views from the Panorama trail are some of the best in Yosemite. It's a great hike and I'm looking forward to doing it again.
If you really want a work out you can hike up the Four Mile Trail that begins near the base of Sentinal Rock and ends at Glacier Point. Then hike the Panorama Trail back down into the valley to Happy Isle. That's a total distance of about 13 miles and will take 10 to 11 hours.
