Of the Baltic Capitals, I rate Tallinn over Vilnius & Riga (in that order). A week should be plenty enough time there.
I’m sure the guide book will direct you to all the nice churches (there are several, plus the Russian Alexander Nevsky ‘Onion’ Cathedral), and the Toompea fortifications are nice to stroll around if the weather’s good (‘Fat Margaret’ & ‘Kiek in de Kok’), with various activities going on there. St Catherine's Passage (Katariina Käik) is a nice old medieval lane, beside the 13th C. Dominican monastery.
‘Hell Hunt’ is a good bar with atmosphere, and the ‘Beer Hall’ on the main square has an enjoyable German-style Bier Keller atmosphere, complete with oompah band and decent food. Make sure to check out the local rocket fuel spirit, ‘Vana Tallinn’.
A bit further afield is the Kadriorg Palace of Peter the Great (which I didn’t do), and if you’re into Motorcycle Road Racing there’s a memorial at the spot where legendary TT racer Joey Dunlop sadly had a fatal accident.
If you have a week in Tallinn and haven’t been to Helsinki before, I’d also recommend a day or overnight trip there via ferry - there’s not a huge amount to see in Helsinki to be honest, but it’s a pleasant place and an easy way to see two capitals in one trip (if you do it on the weekend, you’ll also have the amusing sight of many worse-for-wear hammered young Finns making their way back to Helsinki after taking advantage of a night out on Tallinn’s much-cheaper beer).