Science is becoming data-intensive, requiring new software architectures that can exploit resources at all scales: local GPUs for interactive visualization, server-side multi-core machines with fast processors and large memories, and scalable, pay-as-you-go cloud resources. Architectures that seamlessly and flexibly exploit all three platforms are largely unexplored. Informed by a long-term collaboration with ocean scientists, we articulate a suite of representative visual data analytics workflows and use them to design and implement a multi-tier immersive visualization system. We then analyze a variety of candidate architectures spanning all three platforms, articulate their tradeoffs and requirements, and evaluate their performance. We conclude that although “pushing the computation to the data” is generally the optimal strategy, no one single architecture is optimal in all cases and client-side processing cannot be made obsolete by cloud computing. Rather, rich visual data analytics applications benefit from access to a variety of cross-scale, seamless “client + cloud” architectures.