On the Pest side of the river, the nicest place to wander along is Váci utca (VAH-tsee OO-tsa). It's a pedestrian mall with shops, restaurants, and interesting facades along both sides. It's a great place for people-watching, too. On my first visit, on Saturday, there were plenty of people to see, too. (Later in the week, the place wasn't nearly as busy.)
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