One last thing, I am listing the top boarding schools though I dropped the Black % threshold to 5% since attendance is even more sparse.
First are the four remaining Black boarding schools in the country you can check out
The Piney Woods School
Redemption Christian Academy
Pine Forge Academy
Laurinburg Institute
Boarding school reporting is spotty and some I know of aren't even listed...for example a popular boarding school for Atlanta Blacks in the 90s was Cushing Academy in Ashburnham, MA which is about 7% Black. But below is what they have.
Now the rest by Black enrollment
School Name-----City-----State+Zip-----County-----Total Enrollment-----Black Enrollment-----Black Percent-----4-Yr College Rate
MCDONOGH SCHOOL-----OWINGS MILLS-----MD-----BALTIMORE-----1376-----220-----16-----99
PHILLIPS EXETER ACADEMY-----EXETER-----NH-----ROCKINGHAM-----1073-----123-----11-----99
PRESTONWOOD CHRISTIAN ACADEMY-----PLANO-----TX-----DENTON-----1292-----112-----9-----90
CHOATE ROSEMARY HALL-----WALLINGFORD-----CT-----NEW HAVEN-----854-----80-----9-----99
GEORGE SCHOOL-----NEWTOWN-----PA-----BUCKS-----539-----80-----15-----80
PHILLIPS ACADEMY-----ANDOVER-----MA-----ESSEX-----1142-----78-----7-----99
THE HOCKADAY SCHOOL-----DALLAS-----TX-----DALLAS-----1056-----78-----7-----100
ADMIRAL FARRAGUT ACADEMY-----ST PETERSBURG-----FL-----PINELLAS-----503-----77-----15-----90
ST ANNE'S-BELFIELD SCHOOL-----CHARLOTTESVILLE-----VA-----CHARLOTTESVILLE-----826-----74-----9-----100
CHAMINADE COLLEGE PREP SCHOOL-----SAINT LOUIS-----MO-----ST. LOUIS-----868-----66-----8-----99
THE MASTERS SCHOOL-----DOBBS FERRY-----NY-----WESTCHESTER-----671-----66-----10-----100
SHADY SIDE ACADEMY-----PITTSBURGH-----PA-----ALLEGHENY-----929-----65-----7-----99
WESTTOWN SCHOOL-----WEST CHESTER-----PA-----CHESTER-----712-----64-----9-----100
DARLINGTON SCHOOL-----ROME-----GA-----FLOYD-----693-----61-----9-----97
PEDDIE SCHOOL-----HIGHTSTOWN-----NJ-----MERCER-----544-----61-----11-----100
NORTH CENTRAL TEXAS ACADEMY-----GRANBURY-----TX-----SOMERVELL-----186-----60-----32-----100
THE STONY BROOK SCHOOL-----STONY BROOK-----NY-----SUFFOLK-----412-----57-----14-----99
SUFFIELD ACADEMY-----SUFFIELD-----CT-----HARTFORD-----414-----55-----13-----100
WESTOVER SCHOOL-----MIDDLEBURY-----CT-----NEW HAVEN-----179-----54-----30-----100
THE HOTCHKISS SCHOOL-----LAKEVILLE-----CT-----LITCHFIELD-----603-----50-----8-----100
EPISCOPAL HIGH SCHOOL-----ALEXANDRIA-----VA-----ALEXANDRIA-----450-----47-----10-----99
CATS ACADEMY BOSTON-----BRAINTREE-----MA-----NORFOLK-----460-----46-----10-----100
THE TAFT SCHOOL-----WATERTOWN-----CT-----LITCHFIELD-----600-----44-----7-----100
BEN LIPPEN SCHOOL-----COLUMBIA-----SC-----RICHLAND-----670-----44-----7-----99
NORTHFIELD MOUNT HERMON SCHOOL-----MOUNT HERMON-----MA-----FRANKLIN-----645-----42-----7-----90
THE HUN SCHOOL OF PRINCETON-----PRINCETON-----NJ-----MERCER-----669-----41-----6-----97
WEST NOTTINGHAM ACADEMY-----COLORA-----MD-----CECIL-----81-----40-----49-----99
LINDEN HALL-----LITITZ-----PA-----LANCASTER-----207-----40-----19-----100
THE MADEIRA SCHOOL-----MCLEAN-----VA-----FAIRFAX-----324-----40-----12-----100
BRANDON HALL SCHOOL-----ATLANTA-----GA-----FULTON-----126-----39-----31-----90
EF ACADEMY INTERNATIONAL BOARDING SCHOOL-----THORNWOOD-----NY-----WESTCHESTER-----669-----38-----6-----79
ROSS SCHOOL-----EAST HAMPTON-----NY-----SUFFOLK-----295-----38-----13-----95
THE BROOK HILL SCHOOL-----BULLARD-----TX-----SMITH-----631-----38-----6-----85
ST STEPHENS EPISCOPAL SCHOOL-----AUSTIN-----TX-----TRAVIS-----694-----35-----5-----100
OAKWOOD FRIENDS SCHOOL-----POUGHKEEPSIE-----NY-----DUTCHESS-----143-----34-----24-----100
WESTERN RESERVE ACADEMY-----HUDSON-----OH-----SUMMIT-----390-----34-----9-----100
WOODBERRY FOREST SCHOOL-----WOODBERRY FOREST-----VA-----MADISON-----400-----34-----8-----100
THE ATHENIAN SCHOOL-----DANVILLE-----CA-----CONTRA COSTA-----536-----33-----6-----98
MIDDLESEX SCHOOL-----CONCORD-----MA-----MIDDLESEX-----409-----33-----8-----98
THE LINSLY SCHOOL-----WHEELING-----WV-----OHIO-----468-----33-----7-----97
WORCESTER ACADEMY-----WORCESTER-----MA-----WORCESTER-----574-----31-----5-----98
TABOR ACADEMY-----MARION-----MA-----PLYMOUTH-----536-----30-----6-----99
THE NORTHWEST SCHOOL-----SEATTLE-----WA-----KING-----510-----29-----6-----89
LAKE FOREST ACADEMY-----LAKE FOREST-----IL-----LAKE-----438-----28-----6-----100
THE PENNINGTON SCHOOL-----PENNINGTON-----NJ-----MERCER-----534-----28-----5-----98
ST ANDREWS SCHOOL-----BARRINGTON-----RI-----BRISTOL-----221-----28-----13-----96
BLUE RIDGE SCHOOL-----ST GEORGE-----VA-----GREENE-----170-----28-----16-----100
ST ANDREW'S SCHOOL-----MIDDLETOWN-----DE-----NEW CASTLE-----309-----27-----9-----100
ST JAMES SCHOOL-----HAGERSTOWN-----MD-----WASHINGTON-----223-----27-----12-----100
THE DARROW SCHOOL-----NEW LEBANON-----NY-----COLUMBIA-----102-----27-----26-----97
MERCERSBURG ACADEMY-----MERCERSBURG-----PA-----FRANKLIN-----441-----27-----6-----100
THE KISKI SCHOOL-----SALTSBURG-----PA-----WESTMORELAND-----180-----27-----15-----100
THE STORM KING SCHOOL-----CORNWALL ON HUDSON-----NY-----ORANGE-----194-----26-----13-----100
ST MARGARET'S SCHOOL-----TAPPAHANNOCK-----VA-----ESSEX-----98-----26-----27-----96
PILGRIM SCHOOL-----LOS ANGELES-----CA-----LOS ANGELES-----371-----25-----7-----100
THE WEBB SCHOOLS-----CLAREMONT-----CA-----LOS ANGELES-----406-----25-----6-----100
THE GOVERNORS ACADEMY-----BYFIELD-----MA-----ESSEX-----406-----25-----6-----99
MISSOURI MILITARY ACADEMY-----MEXICO-----MO-----AUDRAIN-----200-----25-----12-----90
CATE SCHOOL-----CARPINTERIA-----CA-----SANTA BARBARA-----297-----24-----8-----100
BROOKS SCHOOL-----NORTH ANDOVER-----MA-----ESSEX-----365-----24-----7-----99
VIRGINIA EPISCOPAL SCHOOL-----LYNCHBURG-----VA-----LYNCHBURG-----261-----23-----9-----96
SOLEBURY SCHOOL-----NEW HOPE-----PA-----BUCKS-----218-----22-----10-----100
THE WEBB SCHOOL-----BELL BUCKLE-----TN-----BEDFORD-----317-----22-----7-----100
THE CHESHIRE ACADEMY-----CHESHIRE-----CT-----NEW HAVEN-----328-----21-----6-----99
EMMA WILLARD SCHOOL-----TROY-----NY-----RENSSELAER-----365-----21-----6-----100
THE KNOX SCHOOL-----SAINT JAMES-----NY-----SUFFOLK-----156-----20-----13-----90
CHRIST SCHOOL-----ARDEN-----NC-----BUNCOMBE-----278-----20-----7-----98
ACADEMY OF THE NEW CHURCH BOYS SCHOOL-----BRYN ATHYN-----PA-----MONTGOMERY-----130-----20-----15-----95
PERKIOMEN SCHOOL-----PENNSBURG-----PA-----MONTGOMERY-----330-----20-----6-----98
SALEM ACADEMY-----WINSTON SALEM-----NC-----FORSYTH-----92-----19-----21-----100
SAN MARCOS BAPTIST ACADEMY-----SAN MARCOS-----TX-----HAYS-----332-----18-----5-----90
SOUTHWESTERN ACADEMY-----SAN MARINO-----CA-----YAVAPAI-----150-----17-----11-----98
LA LUMIERE SCHOOL-----LAPORTE-----IN-----LAPORTE-----183-----15-----8-----81
ST MARY'S SCHOOL-----RALEIGH-----NC-----WAKE-----296-----15-----5-----100
ST ANDREW'S-SEWANEE SCHOOL-----SEWANEE-----TN-----FRANKLIN-----240-----15-----6-----97
WASATCH ACADEMY-----MOUNT PLEASANT-----UT-----SANPETE-----267-----15-----6-----100
HEBRON ACADEMY-----HEBRON-----ME-----OXFORD-----239-----14-----6-----92
STONELEIGH-BURNHAM SCHOOL-----GREENFIELD-----MA-----FRANKLIN-----131-----13-----10-----100
TILTON SCHOOL-----TILTON-----NH-----BELKNAP-----221-----13-----6-----99
KENTS HILL SCHOOL-----KENTS HILL-----ME-----KENNEBEC-----211-----12-----6-----84
WHITE MOUNTAIN SCHOOL-----BETHLEHEM-----NH-----GRAFTON-----131-----12-----9-----100
PURNELL SCHOOL-----POTTERSVILLE-----NJ-----SOMERSET-----46-----12-----26-----100
VERMONT ACADEMY-----SAXTONS RIVER-----VT-----WINDHAM-----169-----12-----7-----95
CHATHAM HALL-----CHATHAM-----VA-----PITTSYLVANIA-----152-----12-----8-----98
FOXCROFT SCHOOL-----MIDDLEBURG-----VA-----LOUDOUN-----173-----12-----7-----100
SUBIACO ACADEMY-----SUBIACO-----AR-----LOGAN-----149-----11-----7-----100
MENAUL SCHOOL-----ALBUQUERQUE-----NM-----BERNALILLO-----196-----10-----5-----79
NEW YORK MILITARY ACADEMY-----CORNWALL ON HUDSON-----NY-----ORANGE-----60-----10-----17-----100
MILLER SCHOOL OF ALBEMARLE-----CHARLOTTESVILLE-----VA-----ALBEMARLE-----190-----10-----5-----99
THE MARVELWOOD SCHOOL-----KENT-----CT-----LITCHFIELD-----102-----9-----9-----95
DUBLIN SCHOOL-----DUBLIN-----NH-----CHESHIRE-----163-----9-----6-----100
OLDFIELDS SCHOOL-----SPARKS GLENCOE-----MD-----BALTIMORE-----89-----8-----9-----90
THOMAS JEFFERSON SCHOOL-----SAINT LOUIS-----MO-----ST. LOUIS-----86-----6-----7-----100
ICL ACADEMY FOR FILM AND PERFORMING ARTS-----LOS ANGELES-----CA-----LOS ANGELES-----16-----4-----25-----86
ACADEMY OF THE HOLY FAMILY-----BALTIC-----CT-----NEW LONDON-----38-----3-----8-----100