THE PLT WAS REPOSITIONING THE ACFT AT NGT TO HIS HOME ARPT AT KINGSTON. HE RCVD VFR ADVISORIES FM NEW YORK TRACON FOR ROUTING TO TETERBORO & TO CONT NORTH BELOW THE TCA, ALONG THE HUDSON RIVER TO KINGSTON. THE ATC CTLR ISSUED A CLNC AS REQUESTED, PROVIDED WX INFO & TOLD THE PLT TO MAINT 2500'. MINUTES LATER, THE PLT REQUESTED A LOWER ALT & WAS APPROVED FOR FLT THRU THE TETERBORO ARPT TFC AREA. HE RPRTD 'THE GEORGE WASHINGTON BRIDGE IN SIGHT' & SAID HE NO LONGER NEEDED RADAR SVC. AT 2222 EDT, RADAR SVC WAS TERMINATED 2 MI EAST OF TETERBORO & THERE WAS NO FURTHER RADIO CTC WITH THE ACFT. SUBSEQUENTLY, IT HIT TREES & CRASHED NEAR A HILLTOP, WHILE HDG SW OVER AN ARTILLERY RANGE ON THE WEST POINT MILITARY ACADEMY. RADAR DATA SHOWED THAT AFTER RADAR SVC WAS TERMINATED, THE ACFT CONTD NORTH BTN 1800' & 1200' MSL UNTIL RADAR CTC WAS LOST APRX 3 MI SOUTH OF THE ARTILLERY RANGE. A WITNESS (2 MI SOUTH OF THE CRASH SITE) SAW AN ACFT CIRCLING AT LOW ALT BEFORE CONTINUING NORTH. SHE SAID CONDS WERE RAINY, CLOUDY & VERY DARK. NO PREIMPACT MECH PROBLEMS WERE FOUND.