The Budapest public transport company BKV continues its boat service on the Danube. At 400 forints (1,5 Euro) per person (and also per bike, and a dog) it is a great alternative to pricy tourist boats. And with colder weather it is at last not so crowded as an Indian train, and one can actually enjoy the ride.
The boat runs from Rákóczi bridge to Rómaifürdő baths with many stops in between. See the route and the times at BKV site.