Modern applications span multiple clouds to reduce costs, avoid vendor lock-in, and leverage low-availability resources in another cloud. However, standard object stores operate within a single cloud, forcing users to manually manage data placement across clouds, i.e., navigate their diverse APIs and handle heterogeneous costs for network and storage. This is often a complex choice: users must either pay to store objects in a remote cloud, or pay to transfer them over the network based on application access patterns and cloud provider cost offerings. To address this, we present SkyStore, a unified object store that addresses cost-optimal data management across regions and clouds. SkyStore introduces a virtual object and bucket API to hide the complexity of interacting with multiple clouds. At its core, SkyStore has a novel TTL-based data placement policy that dynamically replicates and evicts objects according to application access patterns while optimizing for lower cost. Our evaluation shows that across various workloads, SkyStore reduces the overall cost by up to 6x over academic baselines and commercial alternatives like AWS multi-region buckets. SkyStore also has comparable latency, and its availability and fault tolerance are on par with standard cloud offerings. We release the data and code of SkyStore at https://github.com/skyplane-project/skystore.