The World Shakespeare Bibliography is a great database for identifying productions of Shakespeare's The Tempest and it can help lead you to reviews and promotional materials. Some search tips:
Theater production reviews appear in both scholarly and popular periodical sources. Discover searches multiple databases that cover both kinds of sources. It doesn't always do a great job of searching the many subscription news databases that the library subscribes to through ProQuest, so you may also want to search ProQuest News & Newspapers separately to find more reviews from newspapers. Some search tips:
These two databases use the same search interface. Tips for using them to find reviews of plays:
You can also try searching for reviews on the Web using Google. Some search tips: