After a satisfying continental breakfast at the wonderful Savoy Boutique Hotel, I passed through one of the gates in the defensive wall surrounding the Old Town of Tallinn, Estonia, and boarded a tram headed about a mile east to Kadriorg Park. As I stepped off the tram at its last stop, I felt as if I had entered a different world. So close to Old Town but a world away, the street on which I strolled was flanked by gorgeous old wooden mansions resting on rusticated stone foundations, and by sidewalks dotted with delightful bird-shaped stone barricades with heads and tails painted like mallard ducks.

Unlike the UNESCO World Heritage Site just a mile away, this neighborhood is chiefly for locals. But for visitors in the know, its most famous attraction, Kadriorg Park, offers up a full day’s worth of both leisurely activities that entertain and inform, and a reprieve from the tourist-jammed streets and squares of Old Town. And we have a Russian czar to thank for it: This extremely pleasant green space of about 170 acres constituted the grounds of the palace of Peter the Great and has always been open to the public ever since 1718, when he built the royal palace for his wife, Catherine I, after his conquest of Estonia.

I began my exploration of Kadriorg (“Catherine’s Valley,” in Estonian) with a stroll around Swan Pond, a placid body of water encircled by flower beds, benches, and carefully manicured trees. A charming bandstand with dome, arches, pillars, and balustrades stands on an islet in the middle of the lake beside a small fountain that resident ivory-white swans gracefully skirt around.

A little farther along, I noticed several of the palace’s outbuildings, such as the kitchen and guardhouses, that have been transformed into museums and cafés, but the weather was too glorious to be inside, so I headed to the terraced Rose Hill. More than 6,000 yellow, red, white, and pink roses of 32 varieties fragrance the air around Estonia’s largest rosarium and provide a wonderful burst of color amid the greenery and the stone and brick steps and walkways.

Across the street stands the administrative building of the Office of the President. Built in 1938, the two-story pale-peach neo-Baroque structure is embellished with white pilasters on the façade and a front balcony supported by limestone columns. With the national flag on the roof raised, I knew the Estonian president was in town, and the two guards with perfect posture standing at full attention at the front door suggested that this was not a visiting day.

I passed by the modestly sized former home of the czar and czarina, where the couple stayed before the palace was built. Today, this 17th-century summer cottage (the only one left in Estonia) is a museum devoted to the history of the palace and park and includes several of Peter and Catherine’s personal items.

I meandered through a meadow and groves of oak, silver maple, and silver birch trees, and entered the grounds of the Japanese Garden. Added to the park only in 2011, this feature was designed to offer a slow, peaceful journey over stone bridges made in Japan and around two ponds. Even in this tranquil neighborhood, the serenity of the garden seemed heightened, with no dogs, skateboarders, or cyclists allowed. Key to any Japanese garden, a mixture of upright and flat stones are scattered all around, offering plenty of introspective spaces to sit and ponder nature as you admire the reflection of the trees in the water and the orange tiger lilies and bushes of white hydrangea, and perhaps make a friend or two with a finch or red squirrel stopping by to see you.

From the garden, it’s just a short walk to Russalka, the bronze monument on the cusp of a beach on the shore of Tallinn Bay that commemorates the Russian warship of the same name that sank here in 1893, taking all 177 crewmen with her. Erected in 1902, the monument was the first work by a trained Estonian sculptor to be exhibited in the country’s public space. A gray granite base represents the hull of the ship, atop of which stands a granite pillar capped by a bronze angel (the sculptor’s housekeeper served as the model) who holds a cross in her right hand, pointing toward the site of the shipwreck. The pavement around the monument symbolizes a compass and is ringed by cast-iron posts bearing the names of the deceased sailors and ornate lampposts with a double-headed eagle, an important motif in imperial Russia.

The centerpiece of the park is, of course, Kadriorg Palace, and I saved the best for last. I approached the palace via the wonderful Upper Gardens, a genteel space of formal gardens, fountains, and staircases, planned after the model employed at Versailles. Red, white, and purple flowers are snugly tucked into irregularly shaped beds in plots surrounding two fountains. A tall wall at one end, topped by a lengthy balustrade and dozens of urns, features a fountain of Poseidon and his trident as well as small waterspouts—faces look like a cross between a mythological god and a bison, with water streaming from the eyes.

The palace provides a dramatic backdrop to all this, a grand Baroque structure painted white, cream, and deep orange, with a green roof. Peter the Great recruited craftsmen from all over Europe to construct this dignified palace. Although completed in 1718, further improvements to the structure were made later on, including the fantastic ceiling fresco based on Ovid’s Metamorphoses and smaller allegorical paintings that were added to the gorgeous Great Hall, a two-story space rich with intricate stucco decoration (from horn-blowing angels to double-headed eagles topped with three crowns), ornate fireplaces, and Peter and Catherine’s monograms on a deep-blue field—it’s widely considered the most beautiful example of the Nordic Baroque style.

The days of Russia’s high society and intellectuals gathering here eventually faded and came to an end with the overthrow of the moribund Russian monarchy in 1917 and the execution of the Romanov family. Intermittently opened and closed as an art museum over the decades, the palace reopened in 2000 after nine years of restoration as the Kadriorg Art Museum—the only museum in Estonia dedicated to foreign art. Amid the grandeur of the palace, I appreciated some of the museum’s collection of 9,000 works of Western European and Russian painting, sculptures, porcelain, and applied art, such as a beautiful wood frieze depicting the Tallinn cityscape; 16th- and 17th-century religious paintings of the wedding at Cana, Jesus expelling merchants and money lenders from the temple, and the stoning of St. Stephen; and portraits of Russian royalty.

After I emerged from the palace, I made my way back to the tram stop to return to Old Town, delighted to have explored a sublimely beautiful section of Tallinn that has existed—and has been continually evolving—for exactly three centuries.