The integration of DNA into bottom-up nanotechnology has catalyzed a revolution in achieving nanometric precision through self-assembly. This leap forward is instrumental in broadening the horizons for constructing at the nanoscale, harnessing the predictable nature of Watson-Crick base pairing alongside the versatility of interactions such as pi-pi stacking and electrostatic forces. However, this transition to more sophisticated assembly techniques confronts a major obstacle: the decline in predictability. Traditional computational methods, including Molecular Dynamics and Monte Carlo simulations, predominantly offer qualitative insights into the design of DNA nanostructures. This is due to their representations of key phenomena not being sufficiently accurate, leaving a critical gap in the quantitative predictability vital for detailed nano-engineering. This thesis aims to surmount this challenge by refining existing computational models with precise modifications, focusing on coaxial stacking and ion-DNA interactions. It traverses three distinct levels of resolution, each selected to optimally model specific aspects of DNA nanotechnology. A consistent theme across these endeavors is the incorporation of insights from different resolution scales. This multi-resolution methodology fosters a holistic comprehension of DNA nanostructures, facilitating more predictable and accurate nano-engineering. A specific focus is placed on the assembly of 2D structures at the solid-liquid interface, demonstrating how adopting a coarse-grained approach to mechanical representations can significantly improve the predictability and utility of even basic models like the patchy particle model. Moreover, this thesis explores ways to refine the depiction of coaxial stacking and electrostatic interactions within well-known computational frameworks, such as oxDNA and the SIRAH force field. By examining the challenges encountered and the strategies devised to overcome them, this work not only sheds light on the limitations present in existing models but also charts a course for their amelioration. Thus, it outlines a direction for substantial progress in the development of reliable and computationally viable DNA-based nanotechnologies, marking a significant advancement in the field.