We report measurements of meson production in p+p, d+Au, and Au+Au collisions using the STAR detector at RHIC. We compare the yield to the measured cross section in p+p collisions in order to quantify any modifications of the yield in cold nuclear matter using d+Au data and in hot nuclear matter using Au+Au data separated into three centrality classes. Our p+p measurement is based on three times the statistics of our previous result. We obtain a nuclear modification factor for (1S+2S+3S) in the rapidity range |y|<1 in d+Au collisions of R d A u =0.79+/-0.24(stat.)+/-0.03(syst.)+/-0.10(p+p syst.). A comparison with models including shadowing and initial state parton energy loss indicates the presence of additional cold-nuclear matter suppression. Similarly, in the top 10% most-central Au+Au collisions, we measure a nuclear modification factor of R A A =0.49+/-0.1(stat.)+/-0.02(syst.)+/-0.06(p+psyst.), which is a larger suppression factor than that seen in cold nuclear matter. Our results are consistent with complete suppression of excited-state mesons in Au+Au collisions. The additional suppression in Au+Au is consistent with the level expected in model calculations that include the presence of a hot, deconfined Quark-Gluon Plasma. However, understanding the suppression seen in d+Au is still needed before any definitive statements about the nature of the suppression in Au+Au can be made.