How can I filter click-through reports by date range?
There is currently no date filter on the mailing reports.

Adding date filters to the mailing reports and submitting a patch back to core would be one way to solve your problem. https://github.com/civicrm/civicrm-core/blob/master/CRM/Report/Form/Mailing/Clicks.php shows the code that generates the clickthrough report. Adding a date filter to that might not be too difficult to do.

It would end up being similar to the date time filter in the activity report: like the https://github.com/civicrm/civicrm-core/blob/master/CRM/Report/Form/Activity.php#L261 but from the looks of things you'd have to do a bit more playing around with the Report class than just adding it.

The mysql tables you are looking for are civicrm_mailing_event_trackable_url_open (which has a timestap) and civicrm_mailing_trackable_url