Type "mount" at your command line. You'll see a listing something like this:

$ mount
/dev/sda1 on / type ext3 (rw)
none on /proc type proc (rw)
/dev/sda7 on /data type ext3 (rw)
none on /dev/pts type devpts (rw,gid=5,mode=620)
none on /dev/shm type tmpfs (rw)
/dev/sda5 on /tmp type ext3 (rw)
/dev/sda3 on /usr type ext3 (rw)
/dev/sda2 on /var type ext3 (rw)
nfsserver:/vol/office/home on /home type nfs (rw,addr=nfsserver)
nfsserver:/vol/office/log on /log type nfs (rw,addr=nfsserver)
[download]

Each of the /dev/sd\d items is a different disk on your system, and the "type nfs" entries are remote volumes you're connected to.

The system can't operate without / being mounted, so it doesn't make a difference if that's your current working directory. If / is dead, the system definitely needs a reboot anyways, at least.

/var/log (well, /var at least) is usually a separate device, which the system could theoretically live without.

In fact, if your daemon logs via syslog, as such things probably should, the admin can unmount /var/log even if lots of daemons normally log there by reconfiguring syslogd to log somewhere else.

But, in general, /var/xxx is probably an ok 3rd choice, with / being best, and /tmp probably being 2nd.
--
Mike