We describe the design, development and performance of a scanning probe microscopy (SPM) facility operating at a base temperature of 10 mK in magnetic fields up to 15 T. The microscope is cooled by a custom designed, fully ultra-high vacuum (UHV) compatible dilution refrigerator (DR) and is capable of in situ tip and sample exchange. Subpicometer stability at the tip-sample junction is achieved through three independent vibration isolation stages and careful design of the dilution refrigerator. The system can be connected to, or disconnected from, a network of interconnected auxiliary UHV chambers, which include growth chambers for metal and semiconductor samples, a field-ion microscope for tip characterization, and a fully independent additional quick access low temperature scanning tunneling microscope (STM) and atomic force microscope (AFM) system. To characterize the system, we present the cooling performance of the DR, vibrational, tunneling current, and tip-sample displacement noise measurements. In addition, we show the spectral resolution capabilities with tunneling spectroscopy results obtained on an epitaxial graphene sample resolving the quantum Landau levels in a magnetic field, including the sublevels corresponding to the lifting of the electron spin and valley degeneracies.