This will print the latest change date for one file. The -1 shows one log entry (the most recent), and --format=%cd shows the commit date.
See the documentation for git-log for a full description of the options.
You want the "repository wide last commit date for a given git user and git project, for a given branch. For example the date is shown at the top when you visit your repo and go to commits -> master for example:
But as you pointed out, you have to run that command on the machine that performed the last commit. If the last commit date was performed on another machine, the above command only reports local last commit... So:
Doing git pulls is very slow and you're banging GitHub with a heavy operation. Just query the GitHub rest api:
#assuming you're using github and your project URL is visible to public:
# https://github.com/yourusername/your_repo_name
#then do:
curl https://api.github.com/repos/yourusername/your_repo_name/commits/master
That blasts you in the face with a screen full of json, so send it your favorite json parser and get the field called date: