If you want to go on a scenic drive, and you have a few hours to kill--check out Tioga road--drive…read morethrough the pass at just shy of 10k feet, and head down to Mono Lake (which is amazing in its own right). If you want to explore some of Yosemite's best beauty that is far less crowded than Yosemite Valley (but far superior in my opinion), plan to spend some time up in the majestic nature that can only be found along Tioga Road.
In my opinion, this is the best road in all of Yosemite National Park, and is the best way for us in the valley to get from Fresno to Highway 395 when opened. Be warned: This road (aka Hwy 120) is usually closed from mid Autumn (late October through some time in November) until late spring/early summer (May or June most years), as the road traverses some extremely dangerous avalanch zones and is unsafe to plow until the spring thaw hits the snow in the high country.
Also-be warned: There is a lot of wildlife in the high country. Tioga Pass (and Tioga Road) is not a road to speed across. Take your time and savor the beauty of the landscape--high alpine forests, lakes, meadows, granite domes, wetlands--all home to bears, pine martins, mountain lions, bobcats, coyotes, yellow bellied marmots, deer, red foxes, and so many other amazing creatures. Driving fast means you are more likely to have a tragic encounter between your car and an animal that may be trying to cross the road. That and the road meanders some steep curves along some sheer drop-offs. If you aren't careful along the curves, you may find out the hard way that your car doesn't fly. This is definitely a sipping tea type of road, and not one to be mindlessly chugged.
As for provisions, make sure to bring provisions, and also top off your gas tank on either end of the road (either Crane Flat on the western side before you hit Tuolumne Grove, or the Mobile Gas Station/Whoa Nelly Deli on the east side outside of the park boundary--but after you leave hwy 395). There are very limited services between the two ends (usually only in Tuolumne Meadows, but not all services open every year).
Restrooms are also limited. There are some opened seasonally at Crane Flat (indoor plumbing, but closed if the gas station store is closed), Tuolumne grove nearby, Tenaya Lake (pit toilets--pretty gross at the end of the season), Tuolumne Meadows, and a few other spots along the road.
If you plan to do some hiking--especially when the weather is nice, expect to encounter some soggy or wet areas, as some parts of the high country never fully dry out even in the summer months. And mosquitos can be quite wretched. Make sure you bring protection, whether it is bug spray, face nets, long legged and sleeved clothing, or all of the above. Be bear aware as well, and don't store food in your car overnight or in sight during the day.
Also, you should always prepare for weather to change rapidly at these elevations. I've had 70 degree sunny days turn to 40 degrees with hail in as little as an hour.
As a resident of California's central valley and a lover of the high country, I don't consider my year complete until I've gone over Tioga Pass a few times. This truly is a beautiful road. It requires respect, and a little planning....and what it gives in return is usually more than you'd expect.