The superconductor-insulator transition (SIT) is a well-known phenomenon that is observed in many types of superconducting systems, including elemental films and high Tc superconductors. Ultrathin films provide a versatile platform from which to study this ubiquitous, and possibly universal, transition. Two different theoretical approaches have been made to describe the SIT in thin films. The first predicts that Cooper pairs (CPs) exist in the insulating phase, and the second proposes that the transition is driven by pair-breaking, yielding an insulator of localized single electrons. Recent experiments showing the existence of an insulating phase of localized CPs have provided significant support for the first mechanism. This CP insulating (CPI) phase exhibits dramatic transport features including a giant magnetoresistance (MR) peak. Previous work in the Valles lab found such a phase in ultrathin amorphous Bi films quench-condensed onto a substrate with a nanohoneycomb (NHC) hole array. The local Cooper pairing correlations of the CPI phase were evident from Little-Parks-like MR oscillations due to the hole array. This thesis describes investigations of the mechanism for CP localization and the emergence of the CPI phase in NHC films. There are three main results. First, the CPI phase appears to be induced in NHC films by the undulating surface of the substrate, which produces regular spatial variations in thickness that give rise to nanoscale CP islands. Second, the giant positive MR characteristic of the CPI phase emerges with increasing film thickness simultaneously with the MR oscillation signal, associated with local CP phase coherence. The insulating phases of the thinnest films and films in magnetic fields just beyond the MR peak likely consist of CPs totally localized to their islands. Third, amorphous holey films of uniform thickness do not exhibit a CPI phase. These films go from superconductors directly to fermionic insulators with decreasing thickness. These results lend further insight to the nature of the CPI phase and also require at least two classes of SITs: one that can describe the presence of a CPI phase and one that can describe a transition from a superconductor to a fermionic insulator. Advisors/Committee Members: Valles, James, Jr. (Director), Mitrovic, Vesna (Reader), Feldman, Dmitri (Reader).