Barcelona, Brussels, Hamburg, Oslo, Copenhague, Malmo, Budapest, Rome

Here's a suggested itinerary for your 25-day trip to Barcelona, Brussels, Hamburg, Oslo, Copenhagen, Malmo, Budapest, and Rome:

Day 1-5: Barcelona

• Day 1: Start your trip by exploring the Gothic Quarter, La Rambla, and the famous Boqueria Market.
• Day 2: Visit Park Guell, one of Gaudi's most famous works, and enjoy the stunning views of the city from the hilltop.
• Day 3: Spend the day at the beach, soaking up the sun and enjoying the Mediterranean Sea.
• Day 4: Explore the Picasso Museum and the Gothic Cathedral.
• Day 5: Take a day trip to Montserrat, a beautiful mountain range with a monastery and breathtaking views.

Day 6-8: Brussels

• Day 6: Visit the Grand Place, the Atomium, and the Manneken Pis statue.
• Day 7: Explore the Royal Palace and the European Parliament.
• Day 8: Take a day trip to Bruges, a charming medieval town known for its canals and chocolate shops.

Day 9-11: Hamburg

• Day 9: Visit the Elbphilharmonie concert hall and take a boat tour of the harbor.
• Day 10: Explore the St. Michaelis Church and the Miniatur Wunderland museum.
• Day 11: Spend the day at Planten un Blomen park, one of the largest parks in the city.

Day 12-14: Oslo

• Day 12: Visit the Viking Ship Museum and the Akershus Fortress.
• Day 13: Explore the Vigeland Sculpture Park and the Oslo Opera House.
• Day 14: Take a day trip to the fjords, where you can hike, kayak, or simply enjoy the stunning scenery.

Day 15-17: Copenhagen

• Day 15: Visit the Tivoli Gardens amusement park and the Nyhavn harbor.
• Day 16: Explore the Christiansborg Palace and the National Museum of Denmark.
• Day 17: Spend the day at the Frederiksberg Gardens, a beautiful park with a palace and a zoo.

Day 18-19: Malmo

• Day 18: Visit the Turning Torso skyscraper and the Malmö Castle.
• Day 19: Spend the day at the Ribersborgsstranden beach or the Kungsparken park.

Day 20-22: Budapest

• Day 20: Visit the Buda Castle and the Fisherman's Bastion.
• Day 21: Explore the Hungarian Parliament Building and the Széchenyi Thermal Bath.
• Day 22: Take a day trip to the Danube Bend, where you can see the stunning scenery of the river and the surrounding hills.

Day 23-25: Rome

• Day 23: Visit the Colosseum, the Roman Forum, and the Pantheon.
• Day 24: Explore the Vatican City and the Sistine Chapel.
• Day 25: Spend the day at Villa Borghese, a beautiful park with museums, gardens, and a lake.

Remember to book your accommodations in advance to save money and ensure availability. Also, don't forget to try the local cuisine and immerse yourself in the culture of each city!