What's a good 3-day itinerary for Budapest?

Day 1 stays east of the Danube in Pest. Start at the Parliament building at 8:30am, when morning light hits the neo-Gothic facade and the tour groups haven't formed. Tickets run 6,000 HUF for EU visitors, about $19.50. Walk south along the Danube promenade to the Shoes on the Danube Bank memorial, then turn inland to St. Stephen's Basilica, completed in 1905 after 54 years of construction. The observation deck at 65 metres costs 2,000 HUF and gives you Pest's best overhead view. Lunch at Kádár Étkezde on Klauzál tér in the Jewish Quarter. It's a canteen, cash only, weekday lunch only. Paprika-heavy pörkölt with nokedli runs about 3,500 HUF, and the stew smell fills the tiled room before you sit down. Afternoon on Andrássy út. The Hungarian State Opera House, built in 1884, offers 45-minute tours at 3pm and 4pm for 4,500 HUF. Dinner at Menza on Liszt Ferenc tér, where stuffed cabbage or chicken paprikás costs 5,500-7,000 HUF per main.

Day 2 crosses the Danube to Buda. Take the Sikló funicular from the Chain Bridge landing up to the Castle District for 4,000 HUF return. The hilltop quarter is compact, maybe 1.5 kilometres end to end. Walk north to Matthias Church, which dates to 1255 though the current neo-Gothic shell is an 1896 rebuild. Entry is 3,000 HUF. Fisherman's Bastion sits next door. The lower terraces are free, the upper turrets cost 2,000 HUF. To be fair, the upper level gives you the same river view from 3 metres higher, so save the money. Stop at Ruszwurm Cukrászda for coffee and rétes. This pastry shop has operated since 1827, and the walnut strudel arrives warm with powdered sugar that clings to your fingers. Lunch at Pierrot on Fortuna utca 14, where a beef goulash costs about 4,800 HUF. Afternoon at Gellért Thermal Bath on the Buda riverbank, where locker entry runs about 9,000 HUF. The main pool sits under an Art Nouveau glass ceiling from 1918, and the water holds at 36-38°C. The stone tiles feel warm underfoot. Walk up Gellért Hill for sunset, then cross the Liberty Bridge to Ráday utca in District IX for dinner.

Day 3 runs along Budapest's northeast axis. Metro line M1, continental Europe's oldest underground railway since 1896, takes you from Deák Ferenc tér to Hősök tere in 5 minutes for 450 HUF. Heroes' Square was built for Hungary's millennial celebrations that same year. The Museum of Fine Arts stands on the north side, opened in 1906 with a strong El Greco and Goya collection. From the square, walk into Városliget park toward Széchenyi Thermal Bath. This is the big one, 18 pools in a 1913 neo-Baroque complex. Weekend entry costs about 8,500 HUF. The outdoor pool steams in any weather, and you'll hear a half-dozen languages echoing off the yellow walls. Spend 2-3 hours. Late afternoon, take M1 back to the Jewish Quarter for the ruin bar circuit. Szimpla Kert on Kazinczy utca 14 opens at noon daily. The courtyard smells like spilled beer and old wood. It gets packed after 9pm, so arrive by 6pm if you want a table. Dinner at Bors GasztroBar on Kazinczy utca 10, where a pulled-pork soup in bread bowl costs 2,800 HUF.

Buy a 72-hour Budapest travel card at the airport BKK counter for 5,500 HUF, about $18. It covers all metro lines, trams, and buses. Tram 2 along the Pest embankment between Parliament and the Great Market Hall is the city's best sightseeing ride, running every 5-7 minutes with no extra ticket needed. Mid-June temperatures currently sit around 34°C, so carry water and schedule indoor stops between 1pm and 3pm. The walking total across all three days comes to about 25 kilometres. If your legs tire on Day 2, bus 16 runs from Deák Ferenc tér to the Castle District every 10 minutes and is covered by the travel card. One more thing. The Great Market Hall on Fővám tér opens at 6am and closes at 5pm on weekdays. The ground floor has produce and paprika vendors, the upper level has cooked food stalls with lángos for about 1,500 HUF. It sits 400 metres from the Liberty Bridge, so you might add it to the start or end of Day 2.