On August 12, 2002, about 1045 eastern daylight time, a Cessna 172RG, N888RG, was substantially damaged during a hard landing at the Greater Rochester International Airport (ROC), Rochester, New York. The certificated commercial pilot was not injured. Visual meteorological conditions prevailed for the personal flight that departed the Ledgedale Airpark (7G0), Brockport, New York, destined for Rochester. A flight plan was not filed for the flight which was conducted under 14 CFR Part 91. According to the pilot, he departed Rochester about 1000 and flew directly to Brockport. During the flight, he suspected that the airspeed indicator was indicating low for his altitude and power setting, but was not convinced there was a real problem. The pilot landed at Brockport, and then immediately took off again. Once airborne, he decided not to continue the flight as planned, and proceeded back to Rochester. Once in the terminal area at Rochester, the pilot was cleared by the tower controller to land on runway 22. Because runway 22 was the main runway at Rochester, the pilot felt he needed to expedite the landing. The pilot added it "was not due to the controllers or the tower, as they treated me with total professionalism." The pilot characterized the descent rate and airspeed during the approach as higher than "warranted." The airplane touched down, bounced, and then touched down again. The nose of the airplane started to vibrate, and the pilot realized the airplane was damaged. As the airplane cleared the runway, the tower controller radioed the pilot and asked if he was alright, and if he needed assistance. The pilot said yes to both, and shut down the engine. The pilot added that he should not have allowed himself to feel rushed, and that it was a self-induced feeling of urgency. He also felt that he should have initiated a go-around after the first bounce. Examination of the pitot system and airspeed indicator revealed that the indicator was reading within prescribed limits, but was "very" slow to respond to airspeed changes. In addition, the system had numerous leaks, and the technicians who performed the examination felt the leaks were not related to the accident.