Hi Anthony,
I spent 2 weeks exploring the Baltic States a few years ago (2008). We flew Ryanair to Kaunas from where we had pre-booked a hire car online (very cheap). Our itinerary was:
Kaunas
Vilnius
Sigulda
Tartu
Lake Peipus
Tallinn
Helsinki
Saaremaa
Riga
Palanga
Nida (on the Curonian Spit)
Kaunas
We stayed 1 or 2 nights at all these places apart from Lake Peipus and Nida, which we went out of our way to visit en route, and Helsinki which was a day trip from Tallinn.
All these places really warranted far more time but it was fascinating to get an overview of all three countries – they all have their own distinctive characters and seem to be developing independently in different ways.
The places you choose to visit, to fill in the gaps in your itinerary, will depend on your particular interests. I loved Tartu for its history and architecture – it is Estonia's main university town. And nearby Lake Peipus is like an inland sea – we went for a swim from the beach at Mustvee.
The Estonian island of Saaremaa in the Baltic Sea was one of the highlights of the trip for me. Our hostel there was actually a farm - Praakli Farm, near Kärla, in the centre of the island (book through hostelworld.com). We went cycling in the surrounding forests, swimming in forest lakes, and swimming in the sea - from beautiful empty sandy beaches. The castle in the island's capital, Kuressaare, is well worth a visit too.
As a map enthusiast and amateur geographer the Curonian Spit in Lithuania was beckoning to me. We drove right down it as far as the Russian border. From there we were originally going to drive back to Kaunas via the Russian enclave of Kaliningrad but, in the end, since I was travelling with my 3 sons on a tight budget, I decided I couldn't afford the additional cost (and hassle) of 4 Russian visas. We did peer across the border though.
The 3 capital cities are a must for your itinerary, and then Helsinki is so accessible from Tallinn it would be a shame to pass up the oportunity to go there. We got day return tickets for 19 Euros each (as foot passengers) from Linda Line ferries. They often have offers – check out www.lindaline.fi/en/
We bought our tickets the day before we sailed, and got them direct from a Linda Line bureau in one of the department stores in the newer part of town.
A hire car was great for flexibility and exploring off the beaten track. I'm sure you could get a good deal if you booked beforehand on line. I've just checked on travelsupermarket.com, using your travel dates. A medium-sized family car would cost you £292 for 14 days – picked up from, and returned to, Tallinn airport. (You would need to check with the hire company for drop-off at Vilnius.)
Anyway, good luck with your travel plans and have a great trip.
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