Over the last years, the ongoing quest for highly efficient thermoelectric (TE) materials has been centered on nanostructured materials. In particular, two-dimensional (2D) materials have been pointed out to provide a new direction for designing high performance TE devices due to the high sensitivity of their thermal and electronic properties to finite size quantum effects. Thus, we have analyzed here two mechanisms for tailoring the thermoelectric transport properties of novel two-dimensional materials: i) molecular functionalization and ii) structural anisotropy. This study is focused on graphene grain boundaries and 2D puckered materials (phosphorene, arsenene, and SnS monolayers). To do this, we employ a density-functional based tight-binding (DFTB) approach combined with Green's function techniques. Our results show that graphene GBs functionalized with nitrophenyl molecules display higher thermoelectric response than these ones covered with OH and CH3 molecules. Moreover, we have found that puckered 2D materials do not show strong electronic anisotropy, but a strong thermal one, the effect being most pronounced in the case of SnS monolayers. This material also displays the largest figure of merit at room temperature for both transport directions, zigzag (ZT~0.95) and armchair (ZT~1.6). Hence, this work hints at the high potential of these novel nanomaterials in thermoelectric applications.