The Római-part is where Budapest keeps its river casual: a flat, poplar-shaded promenade north of Óbuda where the Danube is for paddling and lunch, not parliaments and bridges. It's the most local stretch of water in the city, and it's best done with nowhere to be.
About four kilometres, best on a Sunday afternoon. Start at Rómaifürdő — named for the Roman bath fed by the same warm springs that pulled the legions north — and drop to the water where the road gives out. The bank is lined with timber csónakházak (boathouses), some a hundred years old, crews out early on the water.
Then the long shaded run under the poplars, the river wide and brown alongside, allotments behind. Halfway down, the lángos stands and terrace cafés: deep-fried dough, sour cream, the river's Sunday food. Below them the bank shelves to gravel where people wade.
The promenade thins towards Óbuda. Cut in to the Aquincum H5, or walk on into the Roman ruins. Look back up the poplars first.