Drupal 7.39 CiviCRM (in this case 4.6.7)
We can't find any way to search for activities with attachments.
Am I missing something obvious?
Similar to this question: Search contacts with attachments
This might be an answer to a slightly different question, but... in the past, I've used a mix of add-ons to perform a full-text search on activities and their attachments:
When you run a search with "Search => Full Text" and filter on activities, it will include any matches in PDFs/DOCs/etc that are attached to activities.
That module may be a significant undertaking (e.g. it requires an extra server, Solr, and the documentation is pretty rudimentary), but if you really need it, it might be a piece in the puzzle.
I've customized the Activity Report to display which activities have attachments. I don't think I added a filter to show ONLY records with attachments, but that's just another line or two of code. I've uploaded a copy to github here: https://github.com/PalanteJon/activityAttachmentReport/tree/master
Note that these aren't the only customizations I've made in this report, but you can search for "attachments" in my code to see how I added attachments to the report.
In the long run we found it easier to add custom attachment fields to Activities.
These are easier to work with in Views and are searchable in the Search Builder.