Mechanically ultrastable environments within maintenance-free dry cryostats are needed for high-precision surface probe microscopy experiments, as well as next-generation quantum technologies. The most demanding applications require picometre-scale precision combined with multi-axis and millimetre-scale scanning range, while offering access to optical, microwave, and radiofrequency control and a vector magnetic field. We demonstrate a versatile platform for such systems based on passive and active vibration control for a commercial dry cryostat. Using a tunable optical microcavity as a sensor, we report vibration levels of 4.2 pm root mean square at 2.3 K over one hour without postselection. We further demonstrate drift-free long-term operation with stability below 8.6 pm RMS over 12 hours. Our system enables continuous and automated operation for next-generation high-throughput applications without the need for liquid helium infrastructure. Requiring only standard machining facilities and commercially available hardware, the design can be readily adapted for cryogenic optical, electrical and magnetic high-precision measurements across quantum science, surface science, and nanotechnology.