RPTR ERROR ADMITTED IN WRONG ARPT APCH UNAUTH LNDG.

Narrative

ON AN IFR PART 91 FLT FROM SFB TO TPF; DSNDED TO 1600 FT. INITIALLY DID NOT HAVE ARPT IN SIGHT. SHORTLY AFTER; I BELIEVED I HAD ARPT IN SIGHT AND WAS LINED UP FOR A STRAIGHT-IN VISUAL APCH TO RWY 21. CONFIRMED WITH CTLR ARPT 12 O'CLOCK; ACCEPTED VISUAL APCH. COMPLETED LNDG CHKLIST. RECONFIRMED MY POS WITH GPS. GPS SHOWED ARPT 210 DEGS AT 3 MI. AFTER LNDG DISCOVERED I HAD INADVERTENTLY LANDED AT MCDILL AFB. GPS STILL SHOWING 210 DEGS AT 3 MI BUT INTERMITTENTLY FLASHING '2 SATELLITES NEED 3.' FACTORS WHICH CONTRIBUTED TO THE MISTAKE WERE: TIME PRESSURE TO PICK UP PAX. BELIEVED ATC HAD CONFIRMED CORRECT ARPT. CERTAIN SENSE OF COMPLACENCY BECAUSE I WAS IN THE IFR SYS. UNFAMILIARITY WITH THE AREA. DEPENDENCE ON GPS. HIGH WORKLOAD PHASE OF FLT; SINGLE PLT. SAME ARPT LAYOUT AT BOTH ARPTS. DISTR DUE TO BUSINESS PROBS. CORRECTIVE ACTIONS: THIS INCIDENT COULD HAVE BEEN AVOIDED BY REFERRING TO A SECTIONAL CHART RATHER THAN PLATES DURING VISUAL APCHS; BY NOT BELIEVING GPS OVER OTHER AIDS; BY NOT DEPENDING ON ATC.