I am looking for more information about which files are most popular on our site. Therefore, I am hoping to see reports showing which files have been downloaded for a given date range. This information is not available in the Admin CP under Statistics > Downloads. Anyone know where I can find this?

Whilst you cannot specify a date range, you can see the most popular of all time, year, month and week by adding the 'top downloads' block from the block manager to anywhere on the front end of your site. Other than the block shown here, there are no reports in which would show you this however.