I have now stayed twice in the Economy Hotel (it has changed its name from the Skane Hotel in the last two years). Both times were comfortable, and very good value (first night I arrived very late and I ended up having to fork out over £100 for a room in a skyscraper where I could barely see the ground - hideous!). I decamped to the Skane next day (now Economy), got 3 nights for what I previously paid for 1 and felt a whole lot happier! Very close to the Old Town, rooms are a decent size with stripped floorboards, which I like ,and free internet. Why can't other European cities do such good value like this?!
No breakfast might be a drawback but it is a reason why it is such good value. There is a cafe over the road where you can get a reasonably priced breakfast or snack all day. The trains fire up very early outside the hotel. I loved it myself, some might not though and should ask for a room toward the back if they suspect they would not.
If in Tallinn a few days you can do another country very cheaply indeed. Come out of the hotel, turn left and follow the main road to the ferry terminal, less than a quarter of an hour walk. A day return to Helsinki, FInland, is less than £30 and takes less than 2 hours. Go early and you can have a whole day in Helsinki.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC