Only on my third try did I find the cloister, and I'm very glad I did. It was a sunny day, and the cloister is secluded and quiet, so I just sat in there for over an hour. There are also medieval religious carvings on display along three corridors inside.
To find the cloister, I had to enter St. Catherine's Passage. If you enter the passage's west end, then shortly on your left you'll see the entrance to Katariina Kirik (currently next to construction). It costs a couple euros to enter the small church turned theatre. The ladies who sold the tickets were only telling some people about the "garden," meaning the cloister, so not even everyone who paid to get into the church knew it was there. If you turn immediately left from the entrance and go right to the end, there are two good-sized bathroom stalls, and a third door that leads into the cloister.
After having glimpsed the cloister from the south windows of St. Peter and Paul's church, I had decided that was close enough, but actually managing to enter the cloister two days later was worth all the trouble of searching for it. It's a beautiful, peaceful place to take a break, sit, and think.