My beloved river is nearly inaccessible here in Budapest. Those busy roads along the Danube (we call them rakpart) are hard to cross. Named after the first Prime Minister of India, Nehru-part is the only public park in the center where you can get close to the water. This is the place where I go to get some peace, because the sense of the river always comforts me. The Nehru-part is always full of relaxing people, children playing, cyclists, runners, dogs etc. Walk around the beautiful flowerbeds or look over the railing by the bank to check the water level and the lively wildlife of the river. At wintertime, my favourite are the crazy-noisy gulls and the skating rink on the north edge (renting ice skates also).
On the south edge, under the bridge, there is a little BMX park. When passing it, I usually stop to watch the extremely skillful children (even 6-8 years old) practicing on their vehicles. Whoa, such a show!
Just next to it, you will find a ferry stop (name: Boráros tér). It is a nice spot to sit on the stairs, and you can continue your sightseeing tour on the boat if the line operates (closed during wintertime, see also: Take the Boat!).
Visit the old oak on the north edge, the most photogenic of all of them here I think.
Nehru-part could be a nice final station on your trip on the tram-N. 2 as well (stop name: Zsil utca, see also: Tram N. 2!).