What's the must-see thing in Budapest?

The Hungarian Parliament Building sits on the Pest embankment at Kossuth Lajos tér, about 800 metres north of the Chain Bridge. Imre Steindl's design took 17 years to build, starting in 1885, and the finished facade stretches 268 metres along the Danube. That dimension means nothing until you stand at Batthyány tér on the Buda side around 8pm in June, when the whole building turns copper-pink and the river reflects it back in wobbling lines. Book the 45-minute English-language interior tour online 2-3 days ahead. Non-EU visitors pay 12,000 HUF (about 39 USD), EU citizens 6,000 HUF (19 USD). The 10am slot tends to be least crowded. Inside, 40 kilograms of gold leaf cover the central staircase vaulting, and the Holy Crown of Hungary sits under the 96-metre dome, lit so the gold seems warm rather than decorative.

Széchenyi Thermal Bath in Városliget is what Budapest does that no other European capital matches at this scale. The complex opened in 1913 in a yellow Neo-Baroque building, and the outdoor pools hold at 38°C year-round, fed by thermal springs drilled to 1,246 metres below the surface. You smell the sulfur 50 metres before you reach the entrance. Go at 9am on a weekday. By Saturday afternoon the main outdoor pool fills with 300 to 400 people, and the sound bouncing off the stone arcade walls turns into a warm, low roar. A locker ticket costs about 8,200 HUF (roughly 27 USD). Bring your own towel or rent one for 3,000 HUF. The interior pools run hotter, up to 40°C, and quieter. The mineral smell stays on your skin for hours afterward. That is not a complaint.

Fisherman's Bastion on Castle Hill in District I gives you the best view in Budapest. Frigyes Schulek built the Neo-Romanesque turrets between 1895 and 1902 as a decorative terrace, not a defensive wall. The upper level charges 2,000 HUF (about 6.50 USD) from March through October, but the lower terrace is free and the sightline is nearly the same. Stand there before 9am and the Parliament Building across the Danube catches the first orange light while the river still looks slate-gray. Behind you, Matthias Church has stood in some form since 1255. The Zsolnay ceramic roof tiles, in diamond patterns of green, orange, and white, are Schulek's 19th-century addition to the Gothic structure. A combined Bastion-and-church ticket runs about 4,500 HUF (15 USD). Tour groups start arriving via the Sikló funicular from Clark Ádám tér around 10:30am. Before that, the terrace is yours.

A note on what to deprioritize. Heroes' Square, completed in 1896 for Hungary's millennial celebration, photographs well but offers about 4 minutes of actual engagement unless you continue into the Museum of Fine Arts next door (opened 1906, worth 2 hours for its El Greco and Raphael holdings). The ruin bars in the Jewish Quarter of District VII are a nighttime draw, not a daytime priority. If your first full day falls in summer, and today's 34°C suggests it might, do Fisherman's Bastion at sunrise, the Parliament tour at 10am, and Széchenyi in the afternoon when hot pavement makes 38°C pool water feel reasonable. The M1 metro, continental Europe's oldest underground railway since 1896, connects Hősök tere at Heroes' Square to Széchenyi fürdő station at the baths in 2 minutes flat.