I nipped over there by ferry for a daytrip because Finland's capital of Helsinki was shut.
I was joined by lots of Finns with suitcases on wheels which they filled with Estonian booze, which is much cheaper than what's on offer from their own state-controlled liquor industry.
But even if you're not in need of cheap booze it's a voyage worth taking for the spectacular views offered of the Baltic with its myriad islands, some barren, others covered with forest, some large enough to be developed as holiday resorts, a few little more than large rocks with just a single cottage sitting alone in the middle of the sea.
And, of course, at journey's end there's a very new country - they don't get much newer than Estonia - and a very old capital.
Tallinn was founded by Danes, who built a fortress on Toompea in 1219, and was fought over since then by Germans, Swedes, Lithuanians, Poles and Russians. Its 14th and 15th century walls and towers, churches and houses, are surprisingly little damaged by all the conflict. Fortunately it is now a Unesco World Heritage site so any modernisation or restoration is done only under strict guidelines.
Vehicular traffic is heavily restricted and most visitors just wander around the narrow cobble-stoned streets enjoying the medieval ambience.
What soon becomes apparent - providing an instant insight into medieval snobbery - is that there were actually two towns, an upper one on top of the hill where the knights and bishops lived in rarefied splendour, their sensibilities protected from the presence of mere merchants and artisans of the lower town by a stone wall.
Both towns were safeguarded from marauding outsiders by an encircling 2.5km long wall with several towers, much of which is still in place today.
The sarcastic sense of humour for which Estonians are famous is apparent in the names of those towers. Peep-in-the-Kitchen Tower was named by folk in the lower town who suspected it had been built so the aristocracy could spy on what they were up to. The Virgins' Tower is where prostitutes used to be confined.
The unkindly named Fat Margaret is an unusually squat tower beside one of the lower gates. Legend tells of a love affair between her and Tall Hermann, the tallest tower of all, who presides over the charmingly pink Toompea Castle, now Estonia's Parliament, at the very top of the hill. Locals claim that on windy nights you can sometimes hear Hermann singing to his love down the hill.
Music is, in fact, very important to Estonians. Apparently they used to protest against Soviet occupation by singing banned folk songs with satirical lyrics. While Czechs talk about their Velvet Revolution, Estonians boast of their Singing Revolution.
There's scope for a bit more satire in the upper town's 14th century Lutheran Dome Church, the oldest in Estonia, which has incredibly elaborate pews, some of them two stories high, the result of one-upmanship between leading families determined to look down on each other.
A slightly more modern piece of pointscoring is represented by the vast Russian Orthodox Alexandr Nevsky Cathedral, at the heart of the old city, built by the Russians to show who was in charge.
There are several spectacular old churches in the lower town, too, the most notable being St Olaf's.
Officially it is named after King Olaf Haraldsson who converted Norway to Christianity. But unofficially the name recalls the legend of a mysterious stranger who offered to build a church with the tallest steeple in the world and to waive his fee if the city fathers could discover his name before the work was done.
In a saga that sounds a bit like the story of Rumplestiltskin, the city tracked down his home and discovered a woman singing to a baby about his father "Olaf".
This news arrived just as the builder was doing the final job, fastening the cross to the steeple, so everyone hurried to the church and called Olaf by name. This so startled the poor fellow that he fell to the ground and died, whereupon a toad and a snake crawled out of his mouth, a sign of evil spirits (and there is in the church a carving of a skeleton encircled by a snake with a toad sitting on his chest).
Whatever the reality of the church's origins, it does seem that for a brief period in the 16th century the 159m spire was indeed the tallest in the world, until it was struck by lightning and burned down, after which it was rebuilt at a safer 124m.
But even with its more modest steeple St Olaf's continued to attract the wrong sort of attention. During the long period of Soviet occupation of Estonia it became notorious as a KGB surveillance centre.
But in many ways the nicest thing about Tallinn is not the grand buildings - which in any case are not all that grand - but the atmosphere it still retains of an olde worlde city.
The crooked lanes of the lower city are lined with beautiful merchants' homes 300 or 400 years old, ancient artisans' shops - most, admittedly, now producing linen, ceramics, glasswork, leather and metalwork for tourists - and quaint cafes.
Among the more intriguing buildings are the three sisters - adjoining houses built by a merchant for his three daughters, the houses' size and decoration reflecting his declining fortunes - the 6th-century old hall of the Great Guild and the headquarters of the marvellously named Brotherhood of the Blackheads, who weren't spotty youths but unmarried foreign merchants.
Strolling round Tallinn you could easily forget that this is the 21st century.
Even the bustling Town Hall Square, where the old town starts to intersect with the shops and offices of the newer areas, has a medieval air.
Partly that's because of the magnificent gothic town hall, a pharmacy whose lineage traces back to 1422 and a clock dating back six centuries.
But I think it's also because of the presence of buxom wenches stirring cauldrons of cinnamon and nuts to sell to passersby - delicious by the way - or the Olde Hansa restaurant where you can eat wild boar off pewter trenchers and drink tankards of honeyed ale.
If food like that has been on offer down the centuries it's no great surprise that Fat Margaret ended up plus-sized.
