In common with many countries in continental Europe, most museums in Tallinn are closed on Mondays, and for many churches they are closed on Tuesdays too. This unusual historic church welcomes visitors throughout the week, for an entrance fee (apart from church services, which are of course free), of 1.50 euros. It is close to the main square in the old town, and I enjoyed my Monday visit so much that I returned with a camera on Tuesday. Not all churches allow photography but it is fine here.
The church is both simple and stuffed full with historic artefacts, including a stunning 16th century altarpiece, which the receptionist kindly suggested I could go behind the rope to see in greater detail.
There are two rather ricketty galleries, and you can climb the wooden spiral staircase to see the stained glass close up. This includes a small (but the largest surviving) collection of historic Estonian glass panels as well as stunning and unusual modern Estonian glass.
The church is Lutheran (protestant) but its interior is much more elaborate than might be expected in the United Kingdom, for example.As others have noted, it is used for concerts and I too heard an organ rehearsal.
I would warmly recommend a visit for anyone wanting an insight into one aspect of Estonian life in the past. As a contrast, the orthodox cathedral on the other side of the old town is also open on Mondays and Tuesdays.