Summer Term ends on 21st June at Edinburgh University. In the last four weeks of term I'd expect that a lot of the students will be busy doing exams, and then they'll be off home.
As for a lack of [christian] activity, I suspect that the Catholic Students' Union, the Christian Union and the Student Christian Movement would take a different view ;-)
Try to get along to a few of the dances that go on. The University society "New Scotland Country Dance" do a social dance every Thursday evening, but there'll be plenty of other dances going on in Edinburgh.
Have a good time. I was in Edinburgh for a couple of years and it was great.