Spectroscopic-imaging scanning tunneling microscopy is a powerful technique to study quantum materials, with the ability to provide information about the local electronic structure with subatomic resolution. However, as most spectroscopic measurements are conducted without feedback to the tip, it is extremely sensitive to vibrations coming from the environment. This requires the use of laboratories with low-vibration facilities combined with a very rigid microscope construction. In this article, we report on the design and fabrication of an ultra-stable scanning tunneling microscope (STM) for spectroscopic-imaging measurements that operates in ultra-high vacuum and at low temperatures (4 K). We start from existing designs with sapphire as the main material and improve the stiffness further by performing finite element analysis calculations for the main components of the microscope to guide design choices on the geometry of the parts. With this strategy, we construct a STM head with measured lowest resonant frequencies above f 0 = 13 kHz for the coarse approach mechanism, a value three times higher than what has been previously reported and in good agreement with the calculations. This allows us to achieve an average vibration level of ∼6 fm , without a dedicated low-vibration lab. We demonstrate the microscope's performance with topographic and spectroscopic measurements on the correlated metal Sr2RhO4, showing the quasiparticle interference pattern in real and reciprocal space with high signal-to-noise ratio.