It's a fairly new road, and doesn't appear on a lot of maps yet (at least, not completely). It does cut off a lot of driving and aggravation for people coming down I-75/Florida Turnpike.
Western Way brings you into Disney right next door to Coronado Springs. If you are staying at All Star Resorts or AKL, turn right when the road dead ends at Buena Vista Drive. For everything else, turn left.
For reference, Buena Vista Drive is the road that runs from DTD, past CBR, past Victory Way (the road to Pop Century), past the entrance to MGM, past the Epcot resorts, over World Drive, past Coronado Springs, past Blizzard Beach, and ends by the All Star Resorts. If you are staying at a MK resort, you would follow the signs for MK which will put you on World Drive (the main Disney entrance road off of 192). For AKL, you will need to exit off of Buena Vista Drive onto the Osceola Parkway westbound (follow the signs to AK/AKL).