Splendours of Budapest, Vienna & Prague

Arrive in Budapest, a city occupying both sides of the Danube River and founded in 1873, when right-bank Buda and Obuda joined left-bank Pest. Budapest's broad avenues and turn-of-the-century architecture have earned it the name, “the Paris of Eastern Europe”. Like Paris, it is a cultural mecca for writers, artists and musicians. Transfer to your hotel, where you join your fellow guests for a welcome dinner. Stay: Four Seasons Hotel Gresham Palace Budapest (D)

This morning, cross the Danube River to explore the Buda side of the city. Visit Matthias Church, the 13th-century coronation cathedral of Hungarian kings, and Fisherman's Bastion, offering spectacular views of the city. Built in neo-Gothic and neo-Romanesque styles, the bastion is named for the guild of fishermen who defended this part of the city during the Middle Ages. Explore the Franz Liszt Academy of Music, with its university and concert hall, founded by the great 19th-century Hungarian composer and piano virtuoso.

Afterward, partake in a Chef's Table experience, joining an esteemed chef for a cooking class in Hungarian specialties, which you then enjoy for lunch. The remainder of your day is at leisure. Stay: Four Seasons Hotel Gresham Palace Budapest (B/L)

Today, discover a different side of the city in Pest. View Heroes' Square and stop to see the Great Synagogue as well as St. Stephen's Basilica, whose south tower houses the largest bell in Hungary. Then, visit the Central Market Hall to explore the vast array of food and crafts on sale throughout its three floors, including cheeses, sausage and other local specialties, and enjoy time at leisure for lunch on your own. Later, visit the Parliament Building before spending the remainder of your afternoon at leisure.

This evening, after dinner, embark on a private cruise of the romantic Danube to watch the glittering lights of Budapest drift by, toasting your journey on a memorable Scenic Sundowner experience. Stay: Four Seasons Hotel Gresham Palace Budapest (B/D)

Journey overland to Bratislava, capital of Slovakia, for a guided walk through its old town, once a jewel of the Austro-Hungarian Empire. Then, embark by high-speed catamaran for a quick cruise along the Danube River to Vienna, Austria. Stay: Hotel Imperial (B/L)

Join your local guide for a walking tour of marvellous Vienna. At the Hofburg Palace — former seat of emperors and current residence of the president of Austria — visit the Imperial Treasury to admire its glittering collection of imperial regalia. Then, continue to the Gothic St. Stephen's Cathedral. Spend your afternoon at leisure. Dine at a local restaurant before attending a concert at the Mozarthaus Vienna, the historic house where Wolfgang Amadeus Mozart lived in the 18th century. Stay: Hotel Imperial (B/D)

This morning, enjoy a panoramic tour of Vienna, viewing the Prater and its Giant Ferris Wheel. See the Secession Building and the famous Hundertwasser House, and then visit the Belvedere Gallery, where you view many works by the brilliant and controversial symbolist artist Gustav Klimt, including The Kiss. Enjoy lunch at a local restaurant, and then visit Schönbrunn Palace, the former residence of Habsburg monarchs. Spend your evening at leisure. Stay: Hotel Imperial (B/L)

Travel to Prague, stopping en route at the Stary Vrch winery in the Czech countryside for a tasting of its signature vintages, followed by lunch. Continue to Prague, where you check in to your hotel, and then enjoy dinner at a local restaurant. Stay: Mandarin Oriental, Prague (B/L/D)

Explore the city's Castle District, starting with the towering, Gothic St. Vitus Cathedral, which houses the tombs of Bohemian kings and Holy Roman Emperors, including that of Wenceslas I, Duke of Bohemia, legendary subject of the beloved Christmas carol “Good King Wenceslas”. Stroll the Golden Lane, the last surviving vestige of Prague Castle's 16th-century architecture, where the castle's original craftspeople lived and worked.

Follow this with a private visit to the Baroque library halls of the Strahov Monastery to view its incredible frescoes, which reside amid detailed stucco ceiling decorations. Stroll in the peaceful quiet, looking up at the mural devoted to the intellectual progress of mankind, and let yourself contemplate a bygone era. Then, admire the religious artifacts at the Loreto Chapel, a remarkable Baroque monument that remains a place of pilgrimage. Cross the famous Charles Bridge, an iconic landmark of Prague completed in 1402.

Break for lunch at leisure, and then enjoy one these Design Your Day activities.

• Attend a Traditional Puppetry Workshop, and then visit the National Gallery Prague in the Schwarzenberg Palace.
• Set Out on a Foodie Walking Tour, savouring tastes of Czech cuisine, from pastries to goulash to beer.
• Relax with a Spa Experience at your hotel, in a haven for the body and spirit, choosing from an array of treatments.

Return to your hotel for an evening at leisure. Stay: Mandarin Oriental, Prague (B)

This morning, set out on a walking tour of Josefov, the city's Jewish Quarter, which remained a walled ghetto until 1848. View the birthplace of Franz Kafka (part of the Jewish Museum complex), best known for his existentialist novel The Metamorphosis. Proceed to visit the Old Jewish Cemetery, site of 12,000 graves, and the Old-New Synagogue, Europe's oldest active synagogue, completed in 1270. Enjoy your afternoon at leisure. Tonight, gather for a celebratory farewell dinner at a nearby local restaurant. Stay: Mandarin Oriental, Prague (B/D)

Transfer to the airport to board your flight home. (B)