For a microscope that involves tracking an atom-thick tip across nanometres of surface, vibrations are not good. STMs often utilize very nice anti-vibration techniques which vary in cost and complexity from simple mechanical dampers to active air or magnetic levitation systems.
For this project I want to explore the possibility of an active vibration-cancelling system, potentially using a continuous 12v air blower to provide a smooth supply of air pressure to actuators mounted on the instrument stage (like the one shown below). The actuators would be 3d printed and use a design which kept the stage supports floating centrally in the stream so as not to make contact with the base at all. If this did not work, then magnets could be used to centre the supports or float the entire stage itself. The weight should be rather small as it only needs to hold a piezo, sample and cantilever.