We report the development of a scanning tunneling microscope (STM), operating at 4.2 K, high magnetic field, and ultra-high vacuum (UHV), and the measurements of Au(111) and NbSe₂ with/without magnetic fields. The STM showed horizontal and vertical scan-ranges of 1.0×1.0 μm² and 270 nm, respectively. As of now, STM measurements have been carried out in a field up to 1 T. The UHV facility for tip/sample preparation in clean environment was integrated into the STM system. The nominal pressure of ~10^-10 mbar in UHV chambers was achieved. However, the data of Au(111) and NbSe₂ were taken before installation of the UHV system. We observed the standing wave of surface state electron of Au(111) by carrying out a conductance map. We found an effective mass of surface state electron of m^* = 0.24m_e, where m_e is the mass of a free electron. We also observed the motion of Au steps when the STM continued scanning. As steps moved, the patterns of herringbone reconstruction on the surface also changed in a complex way. This atomic motion probably resulted from the tip-sample interaction in a stressed film. Using pristine NbSe₂, we observed the charge density wave (CDW) and superconducting states simultaneously at 4.2 K via topographic/spectroscopic measurements. The well-known √3×√3 superstructure of CDW state was revealed in topography. Furthermore, we deliberately introduced two additional phases (√13×√13 and amorphous) by changing a bias voltage from 1-100 mV to 5-10 V. This in situ surface modification can be used in studying the competition between superconducting and CDW states. Lastly, we show that the study of vortex dynamics on the nano-meter scale was achieved by utilizing an extremely slow decay of the magnetic field in the superconducting magnet as the driving source. The field decay rate of ~ nT/s caused vortices to move at ~ pm/s so that the temporal resolution of our STM was sufficient to image these slowly moving vortices. Furthermore, this vortex driving mechanism can be utilized to study vortex dynamics of various superconductors on the nano-meter scale in STM experiments.