How run a script on host without internet?

The script will run on whatever machine you setup the cronjob on. If you setup the cron to run daily on your remote server it will run regardless of if your local internet connection is down or not. If you setup the cron to run on your local machine, it will run locally.

If you have a script you run locally that must speak to / send data to a remote server and you want it to run automatically your local machine must be able to speak to the remote server over the internet.