Terézváros is the Budapest of the Grand Boulevard age — the avenues and café terraces laid out when the city was racing Vienna, anchored by the eight-sided Oktogon and the most ornate coffee house anyone ever built. Do it in the afternoon, when the terraces fill and you can wander into the music academy on a whim.
Start at the Oktogon, where Andrássy út crosses the Nagykörút (the Grand Boulevard) and the yellow trams swing through, then turn down Liszt Ferenc tér for the café terraces and the composer caught mid-stride. The Zeneakadémia sits at the foot of the square: step into the lobby for the gold mosaics, or take a concert if the evening allows.
Cut across Király utca — design shops, ruin bars down the side streets — towards the New York Kávéház, all marble and cherubs, the old writers' café now a queue worth joining for the room alone. End on the boulevard at Blaha Lujza tér, trams and façades, the M2 underfoot.