VPS LCL CTLR ADVISES CL65 FLC THAT THEY ARE DSNDING ON A VISUAL APCH FOR THE WRONG ARPT.

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WE WERE VECTORED BY APCH CTL FOR THE VISUAL TO RWY 19 AT VPS. THE GS WAS NOTAMED OTS. ATC HAD KEPT US A LITTLE HIGH AND WE WERE WORKING ON DSCNT PROFILE AND AIRSPD CTL. THE LOC WAS INDICATING ALIVE AND LITTLE R (W) OF COURSE. APCH CTL ASKED IF WE HAD THE ARPT IN SIGHT -- WE DID; AT 12 O'CLOCK POS. WE WERE CLRED FOR THE VISUAL AND CHANGED TO TWR. CLRED TO LAND; LINING UP FOR RWY 19. AS WE WERE DSNDING; I (CAPT) NOTICED THE LACK OF THE VASI. THE ARPT DID NOT LOOK LIKE WHAT I HAD EXPECTED. THAT'S WHEN TWR CALLED AND SAID IT LOOKS LIKE WE WERE LINING UP FOR DUKE ARPT; 10 MI N OF VPS; SAME RWY ORIENTATION. CTRLINES VERY CLOSE TO BE AN EXTENSION TO EACH OTHER; EXPLAINING THE LOC INDICATION. 2 ARPTS; 10 MI APART; WE HAD ALIGNED UP WITH THE FIRST; SAW THE LOC START CTRING UP; THEN WENT VISUAL; LINING UP WITH THE WRONG ARPT. WE WENT AROUND AT 1000 FT MSL AND LANDED UNEVENTFULLY AT VPS. I CALLED BOTH THE LCL TWR AND COMPANY SAFETY DEPT AND CHIEF PLT FOR DEBRIEFING. I LEARNED TO LOOK IN AND OUTSIDE EVEN FOR THE VISUAL.