An excellent way to start your journey is to visit the splendid Schönbrunn Palace in Vienna, the summer residence of the Habsburgs. Take a stroll around the beautiful gardens, admire the stunning scenery, and soak in the history and architecture of this former imperial palace.
Spend your second day walking around the historical sites of Budapest Castle Hill, one of Hungary's most visited tourist spots. It's a UNESCO World Heritage Site with fascinating attractions like the Royal Palace, Fisherman's Bastion, and Matthias Church that dates back to the 11th century.
For your final day, head to the stunning Danube Bend, where you can experience the beauty of Hungary's countryside. Take a river cruise along the Danube River, marvel at the gorgeous views, or hike up to Visegrád Castle for even more breathtaking scenery.
If you have extra time, explore Austria's capital city, Vienna, or visit more sites in Budapest like the Hungarian Parliament Building or the Széchenyi Thermal Baths. If you have less time, consider skipping Schönbrunn Palace and spending two days in Budapest to see more of the city.