Take a Danube River Cruise.

There is a ferry that the Hungarians use it's part of the public transport there. I took that ferry all over the river with a few of my friends in Budapest last fall -- they live in the city so were very good tour guides ;). Very scenic, there are places to stop and return to the ferry. I found it made an interesting Sunday.

There is a more deluxe evening dinner tour also to see the city, about 50 - 70 euro per ticket, The city is really Buda and Pest the Danube divides the city -- from the river you get an interesting perspective.