While on a 452-mile personal cross-country flight, the 2,800-hour student pilot experienced a problem with the airplane's navigation system and became lost. In order to determine his location and to further examine the navigational system, the pilot selected an airport and elected to land his newly purchased single-engine airplane. During the landing rollout, the pilot lost control of the tailwheel-equipped airplane and the airplane exited the left side of the 4,002-foot long by 75-foot wide asphalt runway. The airplane came to rest in an upright position and the pilot was able to egress the cockpit unassisted. No mechanical anomalies were reported with the airplane's flight controls. The pilot reported having accumulated 100 hours in the same make and model. The pilot further reported that the wind at the time of the accident was a "dead crosswind" at 12 knots gusting to 20 knots.