On July 20, 2005, about 0715 Pacific daylight time, a Cessna 172N, N4961D, veered off runway 12L, struck a ditch, crossed over a taxiway, and hit an airport location sign while landing at North Las Vegas Airport (VGT), North Las Vegas, Nevada. West Air Aviation was operating the airplane under the provisions of 14 CFR Part 91. The student pilot, the sole occupant, was not injured; the airplane sustained substantial damage. The solo cross-country instructional flight departed VGT at 0520, on a round robin flight with an intermediate stop at Mesquite Airport (67L), Mesquite, Nevada. Visual meteorological conditions prevailed, and no flight plan had been filed. The pilot submitted a Pilot/Operator Aircraft Accident Report (NTSB Form 6120.1/2). He stated that after taking off from 67L, he flew direct back to VGT where he did a touch-and-go landing followed by a full stop landing. While doing his touch-and-go landing on runway 12L, he noticed that the landing gear was "abnormally [rough]." He was only on the ground long enough to apply takeoff power and did not think much of the roughness. After takeoff he looked out the window at the left main landing gear tire to see if it was flat but it did not appear to be flat. The pilot set up for a full stop landing in which he leveled off at the numbers and pulled the power to idle. The airplane floated down the runway and the pilot indicated that the airplane stalled just as the main landing gear touched down on the runway. After touchdown the airplane veered to the left and the pilot applied full right rudder and brake, but the airplane did not respond, and exited the runway onto the gravel. The airplane hit a ditch, crossed a taxiway, and hit an airport location sign where the right main landing gear and strut sheared off. The airplane exited the runway prior to reaching the 1,000-foot runway remaining sign. The airport location sign that the airplane struck was located approximately 200 feet off the runway centerline on the south side of taxiway H. The pilot stated that the airplane and engine had no mechanical failures or malfunctions during the flight.