On Friday night, one can camp just outside the west 120 entrance. Take a left turn on Evergreen Road, which is about 1 mile from the entrance. This road goes downhill, and there are several pullouts where you can camp, but the ones near 120 can be rather noisy. You can continue down and across a bridge, then uphill on the other side. Here there are some good pullouts near the top of the hill on the left. For my favorite spot, keep going to the very top, and take a right on Aspen Valley Road. This road quickly turns to dirt with occasional paving; take it for about half a mile to a small intersection/pullout on the right, where there is a green gate. Park there (space for at least 5 cars) and camp in the pine needles on the upill side of the road. When the gate is open, it is also possible to drive through the gate (avoiding a downed tree) and on 200' to further flat areas. No fires are allowed in these areas, incidentally.
The elevation of the "green gate" camping spot is about 4800'. The high point of highway 120 into the park is about 6191' (at Crane Flat). During fall/winter/spring, these elevations may be useful for judging the snow level, and whether chains might be required for entering Yosemite via 120.
There are several other options for camping on Friday night on 120. One which is relatively popular is the Hardin Flat road, which is a right turn off of 120, about 2 miles before Evergreen Road. There are actually 2 signs for Hardin Flat, and people use the second one.
On Saturday night, one can eat dinner at the Lembert Dome Picnic Area, and then drive the 12 miles east to Tioga Pass. Continue east on 120 past the USFS campground at the lake, past Tioga Pass Resort, and past Ellery Lake. Here the road turns left (north) and goes through a big blasted roadcut. At the end of the roadcut, 120 makes a big turn to the right (east) and starts descending through the big talus field. This right turn is at the 9000' elevation level, and there used to be a sign to this effect on the road, but it has since disappeared.
On the left side of the road is a locked brown gate. Just past the gate is a sign which describes the area as "Warren Canyon". You can park off 120 near the gate and walk in 300 feet on a rough road, crossing a small stream at one point. Several free campsites are available here (some with picnic tables); they are nice and quiet.
On the right side of the road, at the same level, you can turn right and get onto the old 120 highway (dirt). You can park immediately on the right at a big level spot with some trees and a nearby stream. Or you can continue down the road (2 switchbacks) and pick another level spot.