Part of the joy is just walking westwards from the centre of town and happening across things, but we found the Patarei prison particularly fascinating, mostly because it hasn't been staged into a museum. It pretty much looks as it did in Soviet times, and even on a warm summer's day (for Tallinn, of course) it's grim and cold inside.
Special note to Instagrammers, especially fans of the Earlybird filter: don't miss the medical wing, which has all kinds of crazy stuff spilling out of rooms. Like old broken Cyrillic typewriters.
Further away from the center of town is the Lennusadam (Seaplane Port), which is also the Estonian Maritime Museum. Which is awesome, fantastically dark, atmosphereic and indoors (great if it's raining or cold), and contains a submarine you can walk around. There's also an old icebreaker ship outside if that's your thing.
Don't feel macabre that the park called Kalamaja Kalmistupark is an old cemetery razed by the Soviets in 1964; the Estonians out walking, running or playing in the park certainly don't. It's a lovely, leafy place, with a few old gravestones in the surviving bell tower.
Top tip for somewhere to eat: fabulous Chinese teahouse and restaurant, Cha Dao, on Suur-Patarei 2. The best Chinese food we've eaten since we were in Hong Kong, seriously.
[Photos: John Walton/Jaunted]