Castle Hill (Varhegy)
Castle Hill is Budapest's most spectacular - and most visited - district. In one small area you have most of the city's big-hitter attractions, including the Royal Palace with its museums and library, the Matthias Church, the Fisherman's Bastion and several spectacular statues. The views over the Danube to Pest are incomparable and worth the trip alone.
Castle Hill has been settled since the 13th century, and you can still feel the scale of the medieval in its steep twisting streets and little square. It's watched over by a magnificent golden turul - the mythical eagle that is featured in Hungarian mythology. As you come up by funicular, the turul is practically the first thing you see.
The Royal Palace also has its fair share of fantastical statues, including a fountain featuring the young King Matthias posing as a hunter. The palace contains the Budapest History Museum and the National Art Gallery as well as the National Library.
The Matthias Church, a blend of styles, mainly dates from the 19th century and is notable for its patterned roofs and elaborate spires. The Fisherman's Bastion, nearby, was built in 1905, and is a fantasy of Neo-Gothic turrets and colonnades. From here you can get what may be the best Castle Hill views of all.
You can walk up Castle Hill, take the funicular or jump on bus 16, which connects with Moszkva Tér, on the M2 line of the Metro. Once up there getting around is mainly by foot, as traffic is restricted. You can take bus 10 or even a horse-drawn carriage ride if you're footsore.