Probably a integrated in-ice Cerenkov + radio neutrino detector with a giant cosmic ray detector (scintillators + water cerenkov tanks + fluorescence detectors + radio) on top, perhaps with some fluorescent/radio detectors deployed on tethered aerostats to look for upgoing air showers from taus. Sort of like IceCube Gen2 Radio on steroids, mishmashed with Auger and ANITA/PUEO/EUSO-SPB. Both in Antarctica and in Greenland to get both hemispheres. But there are arguments for other types of detectors too, and perhaps I'm not thinking big enough since 100 Billion is several orders of magnitude above what is probably reasonable :)
