Kadriorg Palace, built by Peter the Great between 1718 and 1736, now houses a branch of the Estonian Art Museum devoted to Dutch, German and Italian paintings from the 16th to the 18th centuries, and Russian works from the 18th to early 20th centuries (check out the decorative porcelain with communist imagery upstairs). The building is exactly as frilly and fabulous as a palace ought to be and there’s a handsome French-style formal garden at the rear.