“Quaint” it is both quite small and very old, storybook streets of cobblestones and brightly painted houses. Tall towers of stone topped with red tiles.
The old town is a lot like the outdoor museum in Oslo, a place of history. Toompea is this even more distilled.
The public transport is excellent, cheap easy to navigate and pretty modern. The fact there are direct trams to the airport is very helpful.
As you move outside the old town the Russian and Soviet influences becomes more clear. Tsar-ish palaces and brutal soviet concrete war with bright signs of commerce and glass fronted stores of high fashion.
Take a look at Talinn for a more complete outline.