
Tumblr has done away with their Directory (and I don’t miss it). To replace Tumblr’s Directory, there is now a feature called the “Spotlight”. Here’s how you find it:
From your Dashboard, select the “Add and remove” button just below the big, green “Following ‘xxx’ people” button. In the picture below, I’ve circled the Dashboard in green, and the “Add and remove” button is circled in red.

The “Add and remove” page should now be displayed on your screen. That page defaults to the “Spotlight” option. Pictured below is the “Add and remove” page with the “Spotlight” option highlighted in green, and with the selectable Spotlight topics highlighted in a red box.

You can click any of the topics at the right sidebar of the “Add and remove” page to see a display of Tumblrs who are blogging on that topic.
Or if you want to venture “outside the box”, then perform a search with your favorite search engine using the following string in the search box: *.tumblr.com (reads as, “star dot tumblr dot com”) Such a search may or may not show you great Tumblrs, but it will show you popular Tumblrs.