One thing that really helps a school achieve that marquee status, in addition to winning, is a recognizable championship coach with a long track record of winning at the school.
Old Big East had John Thompson, Carneseca, Massimino, Boheim, Calhoun.
Newer Big East had Pitino, Boheim, Calhoun, JT3, Huggins, and to a lesser extent Wright, Dixon, Buzz.

Doesn't mean winning it all multiple times, but having a title and staying long term at the school while creating the perception of always being a contender nationally.

Top level / Considered Marquee Teams
Kentucky - Calipari (1 national title)
Duke - Coach K (multiple titles)
Louisville - Pitino (won titles at both KY and Louisville)
Kansas - Self (1 title)
Michigan State - Izzo (1 title)
Syracuse - Boheim (1 title)
North Carolina - Williams (2 titles)
UConn - Calhoun (3 titles) followed by Ollie (1 title)

Close - But Not Marquee
Arizona (no title since Lute)
Florida (Donovan won 2, but I don't think Florida is a marquee team)
UCLA (legacy has juice, but no longer marquee)
Indiana (legacy has juice, but no longer marquee)

In addition to some deep NCAA runs, the Big East needs winning programs with coaching stability. Win a national title and Jay Wright would be there.