I think it is too late to get reservations in Yosemite NP...the deadline for that period is January 15. However, if you come during the week, you might be able to get a campsite along Highway 140 west of the entrance to Yosemite National Park. If you come in from Highway 140, you can turn left at the bottom of the grade out of Midpines, cross the river, and turn left downstream...you will be on the original railroad roadbed of the Yosemite Valley Railroad, my lifetime interest. There are three campgrounds along this old roadbed although, as I recall, 1 or 2 of them might be walk-ins. We like the most westerly one. I don't recall whether it has water (you can check online...it is BLM campground( but it does have pit toilets. It is an easy drive into the Park from this site.
But, also start trying to get a campsite everyday in the last couple of weeks before you depart...this is the time when people find work interferes with vacations and there is no penalty if you cancel early enough. We got married in Yosemite over a Memorial Day weekend and a couple of people in our party found a room available on that Saturday via walk-up...so you never know.
California has had a lot of snow this year and I doubt that Tioga Pass will be open before Memorial Day. The highway department tries to get it open by that holiday but it all depends on the amount of snow and rocks on the highway. If the pass is open, drop down the far side and turn left onto Highway 395 at Lee Vining. (There is a great sit-down/take out restaurant in the Mobil station just before reaching Highway 395...gourmet food at a gas station!)
After passing through Lee Vining, check out the Mono Lake visitor center and then drive down the lake itsefl.
Further on, turn right at the sign to Bodie (I would think that that road will be clear) and visit the Bodie State Park...they follow the idea of keeping things the way they were but also preventing anymore buildings from falling down. It is a very neat "ghost" town. Google "Bodie State Park" for more information.
There are four roads leaving Bodie...the one you came in on, one which heads northeasterly to Nevada, another which heads south to Highway 167, and one other. Back in the early 1990s, we took the fourth one (which might have been the Bodie-Masonic Road) but we were looking for a place to camp and half-way back to 395 we just turned off of the dirt road and camped on a hillside with a tremendous view of the eastern slope of the Sierra Nevada mounting...4WD not required.
If 395 isn't open yet:
...you can take Highway 140 west to the Big Oak Flat road and then follow Highway 120 back to Highway 49. If Highway 108 is open, you can use it to get to Highway 395 north toward Tahoe. If 108 is still closed due to snow, continue north on Highway 49 through the Gold Rush area and take Highway 88 over the Sierra...this highway stays open all year.
Have a great trip!