In fact, Fitzgerald doesn't want the Judge or the Bureau of Prisons (BOP) to make the designation at all - he wants it left up to the U.S. Marshal's Service:

As for the BOP regulations concerning designation of BOP facilities for the service of civil contempt confinement, by their terms the regulations state that the U.S. Marshal’s Service “has primary jurisdiction in federal civil contempt commitments.” 28 C.F.R §522.11(a). Request by a court for designation is ordinarily because local jails are not suitable because of medical or security reasons. 28 C.F.R. § 522.11(b). The regulations contemplate that referrals to the BOP will be “occasional[].” 28 C.F.R. § 522.10. In any event, confinement of a witness usually should be near the location where the grand jury sits. Thorton, 560 F.Supp. at 185.

Then there's this:

Miller also argues that “while we do not believe we can argue in good faith that Miller’s physical health requires imposition of home detention,” there are certain circumstances which “militate in favor of a home detention setting for health reasons.” Motion at 12. We do not dispute the accuracy of the sealed filings concerning Miller’s health conditions, nor those concerning her husband. Suffice it to say, however, that her health circumstances obtained when Miller was dispatched to Iraq during the conduct of a war. Certainly one who can handle the desert in wartime is far better equipped than the average
person jailed in a federal facility.

Miller argues without elaboration that the D.C. Jail would “be unduly dangerous for a woman in [her] situation.” The motion provides no evidence that the U.S. Marshal’s Service cannot carry out its mission of safely confining a civil contemnor. Special Counsel has no personal knowledge of the conditions in the D.C. Jail for female detainees, or the manner in which the United States Marshals Service and the Bureau of Prisons generally handle civil contemnors in the District of Columbia. Accordingly, Special Counsel defers to the Court’s judgment and experience in determining whether Miller should be confined to the D.C. Jail or some other nearby federal facility. Unless confinement in the D.C. Jail would expose Miller to unacceptable risks, however, it would be inappropriate for Miller to
receive any special treatment not provided to other contemnors.

My Prediction: The Judge will not put her in the D.C. jail. But she may end up in the federal detention center in MDC Brooklyn or MCC Manhattan.

Brooklyn

New York

Another possibility unless the rules prohibit it could be a community corrections facility in Brooklyn or Anapolis- but that's a longshot in my opinion.