The Danube Bend is overflowing with activities to offer day trippers from Budapest. Stop at quaint Szentendre, a former Serbian enclave exemplified by Belgrade Cathedral, and stroll through the old town. This area doubles as a thriving artist colony, which means there’s no shortage of browsing opportunities. Peek into Szentendre’s many galleries and studios located in converted mills and factories and inquire after artisan wares at local market stands in its small squares. When you get hungry, there’s no shortage of Hungarian delicacies and regional wines to sample. If you’re looking for a perfect vantage point, climb the hill to Visegrád, a 13th-century castle town with a stunning view. Next, visit the Renaissance Palace ruins for some open-air history. Be sure to spot the country’s largest basilica at Esztergom, and then ramble the forested chalk cliffs and caves at nearby Pilis Mountains.

Depending on where you go, the trip could be as close as 21 kilometers (13 miles) or as far as 51 kilometers (31 miles) away. Generally, a trip to the Danube Bend can be as quick as 40 or 50 minutes on a high-speed train or an hour by car.

As the favorite residence of Hungary’s 19th-century royalty, Gödöllő is home to the second-largest Baroque palace in the world. Wander around the opulent public spaces and see the decadent private rooms of Queen Elizabeth and her husband, King Francis Joseph. Once you’ve had your fill of palace intrigue, explore the neighboring countryside and traditional farms of the region. For lunch, order a savory scone, called a pogácsa, and a shot of pálinka liquor to unwind before heading to watch a traditional Lipizzaner Horse show.

Fifty minutes by car, or an hour plus journey by train and then connecting to a bus.

A popular resort town on the shores of Balaton, Central Europe’s largest lake, Balatonfürd is a popular destination for relaxation outside of the city. Called the "Hungarian Sea," Balaton features historic waterfront cafés and restaurants, with small shops spread out across town. If you’re looking to get out on the water, rent a boat. For a more adventurous experience, take a ferry or boat tour to nearby Tihany Peninsula where you will discover a Baroque abbey and a stunning panoramic view from twin extinct volcanoes.

While the 135-kilometer (83 miles) journey only takes an hour and a half by car, traveling by combination of train, tram and local bus will take you just under 3 hours.