Urban heat islands (UHIs) and global warming will unavoidably have a negative impact on human health in urban areas, making urban forests much more susceptible to the risk of heat waves than forests. It is pivotal for urban forest management to understand tree species’ adaptation mechanisms by focusing on the species-dependent variability of polyamines (PAs), significant players in the amelioration of biotic and abiotic stress in plants, to mitigate the negative effects of UHIs and global warming on human health. Based on this background, the content of major polyamines (PAs) (putrescine, spermidine, and spermine) and total phenolics and the corresponding antioxidant capacities were determined and analyzed in the 24 most prevalent deciduous and coniferous tree species found in urban areas, namely Futoški Park in Novi Sad (Serbia). High-performance liquid chromatography (HPLC) coupled with fluorometric detection (HPLC-FD) was used to separate and quantify major PAs from tree species. Results showed a species-specific level variation in polyamines, total phenolic, and antioxidant capacity in coniferous and deciduous woody plant species in inspected urban areas. In terms of total PA content, the most notable deciduous tree species were Betula pendula, Junglans regia, and Quercus rubra, while the coniferous tree species Thuja occidentalis, Taxodium distichum, Pinus nigra, and Abies concolor stand out. The most dominant foliar PA in most of the inspected species was putrescine (ranging from 527.67 to 10,049.3 nmol g−1 DW), followed by spermidine (from 250.56 to 2015.92 nmol g−1 DW) and spermine (from 168.8 to 718.41 nmol g−1 DW). Furthermore, significant intra-genus variability in terms of PA content was recorded within the genera Pinus, Thuja, and Picea. This study demonstrated that the PA and phenolic compounds, in combination with antioxidant assays, can serve as reliable and trustworthy criteria and descriptors for the selection of adaptable tree species in the context of urban climate–smart forestry.