I have only been to Tallinn, though I am eagerly anticipating a return to this gorgeous town in May, continuing on to Riga and Vilnius via bus--I will post a trip report, of course. I stayed a week there as I have Estonian heritage and spent a day exploring Rocca al Mare, the outdoor living history museum (which is fun to explore on bikes), a day trip to Helsinki via ferry, a couple of days around town (loved Kadriorg Palace and the KUMU museum, both in the same park near old town) and also really loved the two guided day trips. I used EstAdventures www.estadventures.ee and they offer a nice variety of small-group tours, I went in mid-Sept so was lucky to have the guide, the owner himself, all to myself one day and shared with a charming couple the other. We visited Lahemaa national forest and the Baltic shore, Jagala waterfall, Viru bog, toured some manor houses and a ruined monastery, explored beautiful Haapsalu and a former Soviet missile base, had excellent lunches and he also made a point to take me to a crafts co-op as I am a knitter especially interested in Estonia's famous knitting traditions. For a wonderfully unique souvenir buy some intricately patterned knitted mittens. I never had a bad meal anywhere in old town, and especially enjoyed a pub called Hell Hunt.
I'd like to visit Tartu, but I will say that Tallinn is quite an enjoyable town and has gotten more interesting since I was last there, they have some outlying areas that were formerly industrial that now have markets, food and nightlife, called Telliskivi Loomelinnak (creative city). https://www.tripadvisor.com/Attraction_Review-g274958-d3524330-Reviews-Telliskivi_Loomelinnak-Tallinn_Harju_County.html I'll suggest maybe dropping Tartu and adding either the 2 days to Tallinn, or 1 to Tallinn and 1 to Riga. I am planning 3 days each in the 3 cities.
How are you connecting the dots?