There is a great deal from New York to Budapest. A checked bag is $60 each way. You probably have to get this ticket in the next 24-72 hours. Deals disappear quickly.
Budapest, Hungary’s capital, is bisected by the River Danube. Its 19th-century Chain Bridge connects the hilly Buda district with flat Pest. A funicular runs up Castle Hill to Buda’s Old Town, where the Budapest History Museum traces city life from Roman times onward. Trinity Square is home to 13th-century Matthias Church and the turrets of the Fishermen’s Bastion, which offer sweeping views.