Where can I find the error logs of nginx, using FastCGI and Django?

Errors are stored in the nginx log file. You can specify it in the root of the nginx configuration file:

error_log  /var/log/nginx/nginx_error.log  warn;

On Mac OS X with Homebrew, the log file was found by default at the following location:

/usr/local/var/log/nginx

I was looking for a different solution.

Error logs, by default, before any configuration is set, on my system (x86 Arch Linux), was found in:

/var/log/nginx/error.log

You can use lsof (list of open files) in most cases to find open log files without knowing the configuration.

Example:

Find the PID of httpd (the same concept applies for nginx and other programs):

$ ps aux | grep httpd
...
root     17970  0.0  0.3 495964 64388 ?        Ssl  Oct29   3:45 /usr/sbin/httpd
...

Then search for open log files using lsof with the PID:

$ lsof -p 17970 | grep log
httpd   17970 root    2w   REG             253,15     2278      6723 /var/log/httpd/error_log
httpd   17970 root   12w   REG             253,15        0      1387 /var/log/httpd/access_log

If lsof prints nothing, even though you expected the log files to be found, issue the same command using sudo.

You can read a little more here.