Forest Road 302 starts at Highway 64 inside the town of Tusayan and heads east. Historically, the first 1/4 mile of this road was off-limits to camping, but it seems these days there are often people still camping within this restriction. Still, even when you get past the 1/4 point, there are dozens of previously-used sites to choose from.
This road is very popular with dispersed campers due to it being close to the Town of Tusayan, and being much closer to Grand Canyon Village. There is frequent noise from canyon helicopters flying over throughout the day.
Once you get past the historical 1/4 mile camping limit, you are at the very minimum 7.7 miles (18 minutes) from the South Rim View Point at Grand Canyon Village.
The road itself runs some 16.2 miles east to Lockett Lake. Dispersed camping is allowed the entire distance as long as you do not stray more than 30 feet from the side of the road.
Road conditions is firm packed dirt/gravel and suitable for any vehicle as long as you stay on the road and on previously-used campsites. Otherwise, the ground can get soft.
Kaibab National Forest Order 03-07-01-23-02, Prohibits camping within 1 mile of developed sites in the Williams and Tusayan Ranger Districts, and 1/2 mile in the North Kaibab Ranger District, (eff: September 1, 2023, term: August 31, 2033)