i would suggest running grep only on parts of the filesystem where the string may be found. This depends on what you are searching for.
If you search for something
- you created as any user or user configuration
- /home
- in any programm you installed
- /usr /opt
- anywhere in the logs
- /var
- anywhere in system configuration
- /etc
- your boot files
- /boot
- there are also
- /tmp /mnt /media /root /run/media
- and if you have a lot of time
- /.snapshots /home/.snapshots
But please don’t search in:
- /dev /proc /run /sys
it may not end ever, or even crash
Please have a look at: Filesystem, Permissions:
But there may be also infos for you in:
https://man.archlinux.org/man/file-hierarchy.7
If you had told us what you are searching for, maybe someone would have been able to help you searching in the right place.