A C152 CFI AND STUDENT FIND THEMSELVES ON 'MIL ONLY' TXWY DURING A NIGHT OP AT BAF; MA.

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WE DEPARTED ASH LATE AT PM30. I HAD BEEN AT WORK FOR AN EARLY AM00 FLT SO THIS WAS TURNING INTO A LONG DAY. THE STUDENT HAD SIGNIFICANT PROBS NAVING AND WE WOUND UP ABOUT 20 MI OFF COURSE. IT TOOK HIM 1.6 HRS TO COMPLETE THE FLT FROM ASH TO BAF; A TRIP THAT SHOULD HAVE BEEN DONE IN 1 HR AT THE MOST. WE WERE BEHIND SCHEDULE AND TIRED AT THIS POINT. WE STOPPED TO USE THE RESTROOM AND WHILE WE WERE ON THE GND THE TWR CLOSED FOR THE NIGHT. I HAD BEEN TO BAF BEFORE; BUT NEVER HAD TO TAXI AROUND THE ARPT. I TOOK OUT AN ARPT DIAGRAM AND GAVE THE STUDENT TAXI INSTRUCTIONS TO REACH THE ACTIVE RWY 20. THIS RTE TOOK US ONTO TXWY G. AS WE TRAVELED DOWN THE TXWY I NOTICED THE A10'S PARKED ON THE RAMP AND IT OCCURRED TO ME THAT WE MAY NOT BE ALLOWED IN THE AREA WE WERE IN. I VERBALIZED THIS TO THE STUDENT WHO SAID TO ME THAT 'TWR G IS CLOSED.' I KNEW HE MEANT TXWY; SO I STOPPED THE ACFT AND ASKED HIM TO SHOW ME. I THEN SAW IN THE AFD UNDER ARPT REMARKS WHERE IT SAID 'TXWY G CLOSED TO CIVILIAN OPS.' I LOOKED AROUND AND NOTICED 2 VEHICLES MOVING IN OUR GENERAL DIRECTION. THEY DID NOT APPEAR TO BE COMING AT GREAT SPD AND THERE WERE NO FLASHING LIGHTS; SO I TURNED THE ACFT AROUND AND LEFT THE AREA THE WAY WE HAD COME. WE DEPARTED BAF WITHOUT FURTHER INCIDENT. FATIGUE WAS DEFINITELY A CONTRIBUTING FACTOR TO THIS INCIDENT. I DID NOT LOOK IN THE AFD AND THE PLATE I WAS USING HAD THE RESTR WRITTEN ON IT; BUT IN THE POORLY LIT C152 COCKPIT I FAILED TO NOTICE IT. I DID NOT NOTICE ANY MARKINGS ON THE ARPT ABOUT THE RESTR. I HAVE SEEN A RED LINE ON THE ARPT SURFACE AT OTHER ARPTS AND I KNOW YOU ARE NOT SUPPOSED TO CROSS IT. I DID NOT SEE ANYTHING LIKE THAT AT BAF. IT MAY HAVE BEEN THERE; BUT I DID NOT SEE IT IN THE DARK. WHILE I CERTAINLY RECOGNIZE THAT I SHOULD HAVE SEEN THE NOTES ON MY PLATE SAYING I WASN'T SUPPOSED TO BE THERE; CLRER ARPT MARKINGS WOULD ALSO MAKE THESE AREAS EASIER TO AVOID.