Echoing the style of Kadriorg Palace, this grand building was purpose-built in 1938 to serve as the official residence of the Estonian president. It's currently fulfilling that role once more, so isn't open to the public, but you can take as many photos as you like, and peer through the gates at the honour guards out front.
Sadly, Estonia's first president, Konstantin Päts, didn't get long to enjoy living here. Following the Soviet takeover in 1940 he spent most of his remaining years incarcerated in psychiatric institutions – he was deemed delusional for continuing to maintain that he was the president of Estonia.
