Budapest works best where the city meets its river, and this is the cleanest version of that: the largest market hall in the country, the prettiest bridge, and the embankment promenade that frames Buda across the water. Do it in the morning, when the csarnok (market hall) is for shoppers rather than tour groups and the light is still on the castle.
Begin inside the Nagyvásárcsarnok — three iron-and-glass naves under a Zsolnay-tiled roof, paprika strung in red ropes on the ground floor, lángos griddled on the gallery above. Eat upstairs, leaning on the rail. Out the front, walk to the foot of the apple-green Szabadság híd for the turul birds on its masts, then cut up the quiet lower end of Váci utca for the frontages, not the souvenirs.
Március 15. tér hides a Roman fort under glass; from there, drop to the Duna-korzó and let the castle do the work across the water. End at the Pesti Vigadó, the restored concert hall, with Vörösmarty tér and the little yellow M1 a minute inland.