This paper presents a conceptual space vehicle architecture that could enable human interplanetary travel in progressively more ambitious steps. The main flight vehicle resembles the spaceship Discovery depicted in the novel and film "2001 - A Space Odyssey." Like its namesake, this spaceship could one day transport a human expedition to explore the moons of Jupiter. This spaceship Discovery is a real engineering design that could be implemented using near state-of-the-art technologies, including advanced, bi-modal nuclear thermal rocket (NTR) engines for main propulsion and electrical power. Spaceship Discovery is a modular design: Requirements, features, mass properties, and configuration layouts are presented for each module. Designs for four types of landers are presented, including requirements, mission profiles, performance data, and configuration layouts: (1) A reentry module to return the crew to Earth at the conclusion of a mission or after aborts, (2) a crew exploration lander for Ganymede, Callisto, or Earth's Moon, that utilizes only vacuum propulsive braking, and (3 and 4) Mars exploration crew and cargo landers that utilize both aerodynamic and propulsive braking. Design Reference Missions (DRMs) to the following destinations were used to develop design requirements: (1) Earth's Moon, (2 and 3) Mars, (4) Ceres, and (5, 6 and 7) Jupiter's moons Callisto and Ganymede. The Spaceship Discovery design includes dual, strap-on boosters that enable high-energy Mars and Jupiter DRMs. Mission profiles, performance data, mass properties, and configuration layouts are presented for each DRM, and then compared side-to-side. Launch requirements, mass properties, and module launch configurations are presented. Spaceship Discovery offers many advantages for human exploration of the Solar System: (1) Nuclear propulsion enables propulsive capture and escape maneuvers at Earth and target planets, eliminating the need for risky aero-capture maneuvers. (2) Strap-on NTR boosters provide robust propulsive energy, enabling Mars missions with short transit times and missions to Jupiter. (3) A backup abort propulsion system enables crew aborts at multiple points in the mission. (4) Clustered NTR engines provide "engine out" redundancy. (5) The design provides efficient implementation of omnidirectional GCR shielding using main propellant LH 2 and life support/cooling H2O. (6) The design provides artificial gravity to mitigate crew physiological problems on long-duration missions. (7) The design is modular and can be launched using proposed upgrades to EELVs. (8) High value parts of the vehicle are reusable for Lunar and Mars missions. (9) The LM1, LM2 and LM3 landers are an integral part of the Spaceship Discovery architecture but could be used in other exploration architectures. (10) The design is flexible, with inherent growth capability, and will enable an evolutionary progression to more ambitious missions "to the Moon, Mars, and beyond".