At the rear of the Hilton Hotel, on the Fisherman's Bastion are tables for dining and drinking. To avoid a surprise, check prices before you order. Because of your transit pass, you pay only for that part of the distance outside the Budapest city line. Once you get there, you can travel on foot. This is part of what is called the Danube Bend, including the towns of Visegrad and Esztergom.
Boat trips are also available in all price ranges.
If the price of the fast boat doesn't suit you, try the slow boat. This is a street for strolling, no cars, just people and boutiques. McDonald's and New York City Pizza are nearby if you must. Vorosmarty Ter is located at the foot of Vaci Utca, where you can find the Vigado Concert Hall. Keep going and you will arrive at the Danube River.