Yosemite EntrancesThere are 4 Yosemite entrances -
From the East - you can enter the park via Highway 120 through Lee Vining. The East entrance is called the Tioga Pass Entrance. This entrance is closed from Nov/Dec through May/June. The entrance is 12 miles west of Lee Vining. From the West - you can enter the park via Highway 140 through Merced and El Portal. This Yosemite entrance is called the Arch Rock Entrance. It is about 75 miles northeast of Merced and is the closest entrance to Yosemite Valley.
From the Northwest - you can enter the park via Highway 120 through Manteca. This entrance is called the Big Oak Flat Entrance. The entrance is 88 miles east of Manteca.
From the South - you enter the park via Highway 41 through Fresno and Oakhurst. This is simply called the South Entrance. The entrance is about 64 miles north of Fresno.
The "best" way to get into Yosemite is via Highway 41 because the road is well-paved and it is a relatively easy drive. The last 20 mins or so leading up to the south entrance is pretty winding but not too bad.
The other 3 routes to Yosemite might be okay for drivers and passengers who do not mind winding and steep roads.
If you are prone to car sickness, do take Dramamine or Bonine (whichever works better for you). In the park itself, the roads are winding too in certain areas.