Dynamic task parallelism is a popular programming model on shared-memory systems. Compared to data parallel loop-based concurrency, it promises enhanced scalability, load balancing and locality. These promises, however, are undermined by non-uniform memory access (NUMA) systems. We show that it is possible to preserve the uniform hardware abstraction of contemporary taskparallel programming models, for both computing and memory resources, while achieving near-optimal data locality. Our run-time algorithms for NUMA-aware task and data placement are fully automatic, application-independent, performance-portable across NUMA machines, and adapt to dynamic changes. Placement decisions use information about inter-task data dependences and reuse. This information is readily available in the run-time systems of modern task-parallel programming frameworks, and from the operating system regarding the placement of previously allocated memory. Our algorithms take advantage of data-flow style task parallelism, where the privatization of task data enhances scalability through the elimination of false dependences and enables finegrained dynamic control over the placement of application data. We demonstrate that the benefits of dynamically managing data placement outweigh the privatization cost, even when comparing with target-specific optimizations through static, NUMA-aware data interleaving. Our implementation and the experimental evaluation on a set of high-performance benchmarks executing on a 192-core system with 24 NUMA nodes show that the fraction of local memory accesses can be increased to more than 99%, resulting in a speedup of up to 5× compared to a NUMA-aware hierarchical work-stealing baseline.