I am the one who knows something about Estonia, having translated five books of literature by Jaan Kross, Mati Unt and Friedebert Tuglas from their language. I should be there now on a translators' conference, but couldn't make it. (Look the above authors up with the name "Eric Dickens" on the net; it's not my fault I myself have a literary surname.)
But down to business:
Your trip is a long one, visiting many countries, so the first question is how many days are you prepared to spend in a country slightly larger than the Netherlands, that spent over half a century in Soviet captivity, but is now very computer literate, has a beautiful big bookshop in the capital, but still suffers, in the suburbs, from the chaos and neglect left as a legacy by the Soviet Union? Monty Python actor Michael Palin, in his recent programme, highlighted rather eccentric people. Kirsty Wark was slightly better. The vast majority, both Estonian- and Russian-speaking, are more normal than you would imagine, when Brits go to peer at the natives.
Tallinn. Mediæval city walls. Upper Town and Lower Town in the old city. Nice town square with tables to eat and drink at in sunny weather. Nice big shopping centre. Parks, museums, concerts. Hotels generally up to Western standards (unless you're sleeping on board ship). There's an excellent little travel guide in pocket format in the Footprint series by Clare Thomson:
http://www.buy.com/prod/footprint-ta.../35239931.html
or
http://www.amazon.co.uk/Footprint-Ta.../dp/1903471982
This guide also briefly covers Tartu and Pärnu.
Tartu. University city. Lively during term-time. A good deal smaller than Tallinn. Your namesake, Oscar, is sitting permanently in bronze form on a park bench with his namesake - the Estonian realist novelist Eduard Wilde (spelt Vilde nowadays). I have just been translating a story by this latter author.
Pärnu. The seaside resort of Estonia, termed, for some reason "The Summer Capital of Estonia".
The literature is described and excerpted at:
http://www.estlit.ee/?id=2
and
http://elm.einst.ee/