Tallinn was my first solo trip to Europe in September 2013 (and I returned in 2019 because it is fabulous! Added Riga and Vilnius that trip) and I spent a week, taking the Tallink Silja ferry to Helsinki for a long day trip. It is definitely worth it, the city is beautiful and clean and I caught a bus from the ferry terminal that took me to Kauppatori esplanade where there was a great outdoor marketplace to explore, and from there I took the short boat ride out to Suomenlinna sea fortress, an island that is full of interesting things and I spent perhaps 3 hrs there. Back in Helsinki proper I ended up in their downtown area, this felt a bit like San Francisco to me...in a good way. A big fan of Marimekko designs and the Moomins of Tove Jansson, I was delighted to find their shops before having an early dinner and heading back to the ferry. As a newbie to Europe I was perhaps not as adventurous as I am now so there's definitely more to do in Helsinki.
If you tire of Tallinn's glorious old town (I really don't think it's possible), consider a tour that takes you to nearby towns such as Haapsalu or the Lahemaa national park. I used EstAdventures and they focus on very small groups so my 2 day trips were very personal and satisfying.