You'd have to write an application on your host platform to write files to a MicroSD / SD Card.
Embedded Linux would likely facilitate this by way of the usual C STDIO functions for files, and on STM32 like platforms the use of FATFS and a SDMMC/SDIO interface layer.
What exactly you write to your files is up to you. The NMEA sentences as basic ASCII, you could write those as lines, perhaps buffering for efficiency. Or you could perhaps process the data and output a more compact form expressing latitude, longitude, etc in a different ASCII or Binary record form.
