Discrete time crystalline phases have attracted significant theoretical and experimental attention in the last few years. Such systems require a seemingly impossible combination of nonadiabatic driving and a finite-entropy long-time state, which, surprisingly, is possible in nonergodic systems. Previous works have often relied on disorder for the required nonergodicity; here, we describe the construction of a discrete time crystal (DTC) phase in nondisordered, nonintegrable Ising-type systems. After discussing the conditions for interacting and periodically driven systems to display such phases in general, we propose a concrete model and then provide approximate analytical arguments and direct numerical evidence that it satisfies the conditions and displays a DTC phase robust to local periodic perturbations.