Belváros is the oldest skin of Pest, and the trick to it is to do the inner city and the river as one loop rather than treating the shopping street as a destination. Under three kilometres, best in the morning before Váci utca fills and the café terraces take the square.
Start on Vörösmarty tér with the poet's monument in white marble, then step into Café Gerbeaud — you don't need the full sit-down ceremony; a coffee and a look up at the ceilings will do. From the square, Váci utca runs south, pedestrian the whole way; walk the upper half slowly and let the lower half thin out. Detour to the Párisi udvar, a glass-domed arcade that is the oddest interior in the inner city, then cut west to the water at Vigadó tér.
The river is the payoff. The Danube opens at your feet, Buda Castle and Gellért Hill across it, the Chain Bridge to your right. Walk the korzó north along the embankment, then turn inland to Vörösmarty tér and the little yellow M1 home.