The progress of modern electronics largely depends on the possible emergence of previously unknown materials in electronic technology. The search for and combination of new materials with extraordinary properties used for the production of new small-sized electronic devices and the improvement of the properties of existing materials due to improved technology for their manufacture and processing, in general, will determine the progress of highly promising electronics. In order to solve the problematic tasks of the miniaturization of electronic components with an increase in the level of connection of integrated circuits, new forms of electronic devices are being created using nanomaterials with controlled electrophysical characteristics. One of the unique properties of fullerene structures is that they can enclose one or several atoms inside their carbon framework. Such structures are usually called endohedral fullerenes. The electronic characteristics of endohedral fullerenes significantly depend on the properties of the encapsulated atom, which makes it possible to control them by choosing the encapsulated atom required by the property. Within the framework of the density functional theory in combination with the method of the nonequilibrium Green’s functions, the features of electron transport in fullerene nanojunctions were considered, which demonstrate “core–shell” nanoobjects, the “core” of which is an alkali halide crystal—KI—and the “shell” of which is an endohedral fullerene C180 located between the gold electrodes (in the nanogap). The values of the total energy and the stability diagram of a single-electron transistor based on endohedral fullerene (KI)@C180 were determined. The dependence of the total energy of fullerene molecules on the charge state is presented. The ranges of the Coulomb blockade, as well as their areas associated with the central Coulomb diamond were calculated.