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Hospital inpatient care costs is the largest component of health care expenditures in the US. At the same time, the number of non-hospital rehabilitative settings, such as skilled nursing facilities (SNFs), has increased. Lower costs and increased availability have made SNFs and other non-hospital rehabilitation settings a promising care alternative to hospitalization. To maximize their benefits, transitions to SNFs require special attention, since poorly coordinated transitions can lead to worse outcomes and higher costs via unnecessary hospital readmissions. This study presents a framework to improve care transitions based on the premise that certain SNFs may provide better care for some patients. We estimate readmission rates by SNF and patient types using observational data from a tertiary teaching hospital and nearby SNFs. We then analyze and solve a stochastic model optimizing patient transfer decisions to minimize readmissions. Our model accounts for patient discharge patterns and SNF capacity availability. We provide conditions for when an easy-to-use myopic policy, which assigns discharged patients to the SNF with the lowest readmission rate that is available, is optimal. We also show when an optimal policy has a threshold-like structure. Using estimated readmission rates, we compare the performance of the myopic policy and a proposed policy that depends on the discharge process, readmission rates, and future SNF availability. We evaluate when the myopic policy may be beneficial to use and when the proposed transfer heuristic provides a better alternative. Otherwise, we contend that using a stochastic optimization model for guiding transfer decisions may help reduce readmissions.