Head first for the historical town of Esztergom, Hungary’s former capital and the seat of its Catholic church. Here, visit the imperious Esztergom Basilica, a massive green-domed edifice that’s Hungary’s biggest church and visible for miles around. Go inside to admire the interior with its Renaissance motifs and paintings.

Explore the restored chambers of Visegrád Royal Palace, a seat of royal power during the 1400s, and visit the walled 13th-century citadel, a hilltop fortress-palace that once held Hungary’s crown jewels. Savor the bird’s-eye views of the Danube Bend from the ramparts, and then refuel with a delicious 3-course lunch, drink, and coffee at a charming river-view restaurant.

Travel south to Szentendre, a historical town overlooking the Danube that's known as an artists’ community. Absorb the relaxed Mediterranean-style atmosphere on a stroll through the cobbled streets and admire the prettily painted baroque houses, churches, and museums. Relax over coffee and cake (own expense) at one of the quaint cafes, and enjoy time to visit one of Szentendre's museums or shop for arty souvenirs in the enticing gift shops and galleries.