A CE550 CREW LANDED ON THE WRONG RWY AT TEB.

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NIGHTTIME; VFR ON AN IFR FLT PLAN; SHOOTING A VOR/DME-A APCH INTO TEB; NJ. BOTH PLTS WERE UNFAMILIAR WITH THE AREA; ESPECIALLY AT NIGHT. WE DID NOT GET SWITCHED OVER TO TWR FROM NEW YORK APCH UNTIL WE ASKED; RIGHT OVER THE TOP OF TEB. I RECALL LOOKING R DOWN AT RWY 24 LIGHT BRIGHTLY. AS I TURNED DOWNWIND; TWR RECEIVED OUR CALL AND CLRED US TO LAND #2. I UNDERSTOOD IT TO BE RWY 24; I WAS THE PLT FLYING. AS WE CONTINUED DOWNWIND; BOTH PLTS' ATTN WERE OUTSIDE THE COCKPIT LOOKING FOR OTHER ACFT; OBSTACLES; AND TWRS. THE PNF SAID; 'HILL AT 12 O'CLOCK POS AND TWR.' AT THAT POINT I STARTED A L BASE TURN FOR RWY 24 AND CONTINUING ONTO FINAL; CALLING FLAPS TO LAND; CONTINUE CHKLIST. PNF SAID CHKLIST COMPLETE EXCEPT FOR YAW DAMPER; WHICH I THEN DISENGAGED; THEN CALLED CHKLIST COMPLETE. AN AIRPLANE WAS JUST DEPARTING RWY 24 AT TEB AS WE WERE ON ABOUT A 2 MI FINAL. I THEN ASKED PNF TO VERIFY WE WERE CLRED TO LAND. TWR SAID; 'ROGER; CLRED TO LAND.' AFTER WE LANDED AND EXITED THE RWY; THE TWR THEN SAID WE WERE SUPPOSED TO LAND RWY 19 (SOLUTION). WE SHOULD HAVE BEEN SWITCHED TO TWR EARLIER; TWR SHOULD HAVE MONITORED US CLOSER IF WE WERE SUPPOSED TO LAND RWY 19 INSTEAD OF RWY 24; ESPECIALLY WHEN WE VERIFIED CLRED TO LAND ON A 2 MI FINAL FOR RWY 24. THAT PARTICULAR VOR DME-A APCH TO A VISUAL WHERE 2 RWYS INTERSECT SO CLOSELY; SHOULD NOT BE ALLOWED. AS PLTS; WE SHOULD HAVE COMMUNICATED BETTER AND BEEN LOOKING INSIDE AS WELL AS OUTSIDE -- NOT JUST OUTSIDE. WHEN YOU'RE ON A VISUAL; YOU DON'T WANT TO RUN INTO ANYTHING.