Heavy quarkonium production is not fully understood, but often described by two different models, the Color Singlet Model (CSM), and the Color Octet Model (COM). Previous measurements at the Tevatron collider by the CDF and D0 experiments are not fully in agreement with predicted observables from either model. The Relativistic Heavy Ion Collider (RHIC), and the Solenoidal Tracker At RHIC (STAR) is well suited to further explore heavy quarkonium production. The Heavy Flavor program in STAR encompasses various heavy-flavor analyses, taking advantage of its large solid-angle acceptance, including measurements that explore the properties of heavy quarkonium production using J/ψ and Upsilon (Υ) reconstructions via the di-electron channel, in p+p, d+Au, Cu+Cu, and Au+Au collision systems. This thesis presents results of reconstructed Upsilon (Υ) to study the Upsilon(nS) [n = 1, 2, 3] line- shape and measurements of the production-related observables of spin-alignment (‘polarization’) and Upsilon + hadron correlations (Υ + h) to investigate the Upsilon production mechanism, using triggered data from Run-8 (2008) d+Au and Run-9 (2009) p+p collisions at sqrt(sN N) = 200 GeV, detected at STAR. The result of the spin-alignment measurement is α = 1 ± 0.3 with χ^2 /n.d.f. = 18.71/7 indicating a large (transverse) polarization. The measurement of hadronic activity near the vicinity of an Upsilon, within current uncertainties, is in reasonable agreement with both CSM and COM predictions from PYTHIA, but slightly favors the COM prediction for the near-side Υ + h correlation.