Forecasting Multiple (few hundreds) uni-variate time series with inflated zeros
I can suggest auto.arima function from forecast library, if you are R user, if you are Python user then follow this link. All you need is to write simple for loop, which allows you to built best ARIMA models in different geographic locations:

   for (my_time_series in set_of_all_time_series){
        model=auto.arima(my_time_series )
         }

You can cluster your time series by correlation (make sure that your time series are stationary to avoid spurious correlation). If this reduces the number of time series (which will depend on threshold on correlation), you can take any 1 member from each class, build any model (not only ARIMA) and apply model results on each member of that class.
Contract VAR model