Three best players on every UConn team from 1986/87 through 2006/07:
86-87: Cliff Robinson (upstate New York), Jeff King (Michigan), Phil Gamble (Washington, D.C.)
2 out of 3 from regional recruiting grounds.
87-88: Robinson, Gamble, Tate George (Newark, NJ)
3 out of 3 from regional recruiting grounds
88-89: Robinson, Gamble, George
3 out of 3 from regional recruiting grounds
89-90: Nadav Henefeld (Israel), Chris Smith (Bridgeport), George
2 out of 3 from regional recruiting grounds.
90-91: Smith, Scott Burrell (New Haven), Rod Sellers (South Carolina)
2 out of 3 from regional recruiting grounds.
91-92: Smith, Burrell, Sellers
2 out of 3 from regional recruiting grounds.
92-93: Donyell Marshall (Pennsylvania), Burrell, Brian Fair (Arizona)
2 out of 3 from regional recruiting grounds.
93-94: Donyell, Doron Sheffer (Israel), Ray Allen (South Carolina)
1 out of 3 from regional recruiting grounds.
94-95: Ray, Doron, Kevin Ollie (Los Angeles)
0 out of 3 from regional recruiting grounds
95-96: Ray, Doron, Travis Knight (Utah)
0 out of 3 from regional recruiting grounds
96-97: Richard Hamilton (Pennsylvania), Rashamel Jones (Stamford), Ricky Moore (Georgia)
2 out of 3 from regional recruiting grounds.
97-98: Hamilton, Khalid El-Amin (Minnesota), Kevin Freeman (Massachusetts/New Jersey)
2 out of 3 from regional recruiting grounds.
98-99: Hamilton, El-Amin, Freeman
2 out of 3 from regional recruiting grounds.
99-00: El-Amin, Freeman, Albert Mouring (Maryland)
2 out of 3 from regional recruiting grounds.
00-01: Caron Butler (Wisconsin), Mouring, Edmund Saunders (Waterbury)
2 out of 3 from regional recruiting grounds.
01-02: Butler, Emeka Okafor (Texas), Ben Gordon (Mount Vernon, NY)
1 out of 3 from regional recruiting grounds
02-03: Okafor, Gordon, Taliek Brown (New York City)
2 out of 3 from regional recruiting grounds.
03-04: Okafor, Gordon, Brown
2 out of 3 from regional recruiting grounds.
04-05: Charlie Villanueva (New York City), Josh Boone (Maryland), Rudy Gay (Maryland)
3 out of 3 from regional recruiting grounds
05-06: Gay, Boone, Marcus Williams (Los Angeles)
2 out of 3 from regional recruiting grounds
06-07: Jeff Adrien (Boston), A.J. Price (Long Island), Jerome Dyson (Maryland)
3 out of 3 from regional recruiting grounds
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In total, that's 32 players from the first 20 years who spent at least a season as a top 3 player on the team, and thus fall into the "best players" discussion. Of those 32, 19 were from New England, the mid-Atlantic or DMV.