When I was younger, a drive of a bit over 500 miles would be a walk in the park. Now, not so much. I need to stop more often to walk a bit and give my back a break. Then you'll also have to factor in the time needed for gas/food/pit stops. As the other respondents have pointed out the time needed to complete your trip will largely depend on if Tioga Pass is open. If it's not this is a two day trip at best.

Most mapping routines are pretty good at finding the 'best' routes and often will suggest other alternatives as well. But the thing you have to remember is that 'best' as defined by computer algorithms means shortest and/or quickest. Also, in the absence of any other information, they will assuming that you will be travelling at the sp0eed limit, will see no stop lights or other traffic. Some will note if there is known construction going on, but it's up to you to make corrections to your time in the road. I typically add about 10% to the predicted time to account for traffic. I usually do better than that, but I'd rather arrive earlier than expected than later. And don't forget to add in the time for any sight-seeing, exercise, or meal breaks you'll be taking.

So bottom line, I'd make two plans, one for if Tioga Pass is open (9+ hours via Cedar City, Crystal Springs, Tonopah and Benton; and a second that continues north on US-395 along the western shore of Mono Lake and then over the mountains using CA-108 before hooking back in to Yosemite on CA-120. The latter route would take close to 13 hours (plus stops) and so is not doable in a single day.

AZBuck