Road up Yankee Boy has recently been improved as of 2018. The shelf sections are now smooth & graded. There should be no issues for passenger vehicles to continue up to the start of the 4x4 section at the Governor Basin road turnoff (just past the Atlas Mill) other than the washboarded switchbacks and unrelenting steepness.
To access this trailhead, head south out of Ouray on Highway 550 up Red Mountain Pass for 0.4 miles. At the first switchback, take a right onto Ouray County Road 361 (aka 'Camp Bird Road")—a graded dirt road. Immediately after this turn, the road branches with the right fork taking off toward Box Canyon Falls. Take the left fork, (just continue straight ahead actually) which will lead you on a bridge over the creek before beginning the relentless climb up into Yankee Boy Basin. Continue past the turnoffs for Camp Bird Mine & Imogene Pass and across the famous, spectacular shelf section of the Yankee Boy Basin Road (CR 26). Keep going until the road branches to Governor Basin around mile 7.75. Passenger cars shouldn't have any issues making it to this point (usually).
NOTE: The best parking may be just before the Governor Basin Road turnoff back near the Atlas Mill.
If you're driving a 4x4 vehicle, continue right farther up the Yankee Boy Basin Road for approximately another 0.9 miles to a large pullout with a solar vault toilet at around 11,380'. The 4x4 road up to the bathroom is in great condition as of 2018 as well—no obstacles of any real significance. A little clearance and low gears are helpful, but there should be no difficult maneuvers up to the trailhead that a stock 4x4 can't handle. Even some crossover vehicles should be able to make it if driven carefully.
The only camping allowed in Yankee Boy basin is now restricted to Thistledown and Angel Creek Campgrounds. As of June 2018 the Angel Creek Campground was temporarily closed "due to hazard trees." At Thistledown, there is an overflow area on the north side of the road just past the main campground thta has three or four other sites which are "walk-in" sites.
About 100 yards past the solar vault toilet, a road turns off to the left that drops down a little, crosses a larger puddle and then swings up into an area of trees. There are about five primitive campsites in among these trees. IN 2018, we observed on two separate weekends, various groups openly camping here with tents & RV's. We are not sure if using these spots is truly permissible or not. One Forest Service ranger told us that camping on FS land is not permissible anywhere in the basin, however, she also pointed out that there are all kinds of old claims in this area that are not considered FS land and that some of these areas could be used for camping. That may be the case with the spot described here, however if not on FS land, then you are on a private holding of some kind. On another trip, our son saw several people up at the various turnouts on the 4x4 section camping in their vehicles, but no tents. When he returned to the car after his climb, there was a woman associated with a Yankee Boy Basin conservation group who was checking the area round the restroom and also the trail and level area above it for signs of camping usage. She was photographing and documenting everything. Camp at your own risk on this one!