Budapest is 23 districts, divided into Buda, which has 6 districts, and Pest, which has 16. Buda and Pest are divided by the Danube River. Then there is a district on Csepel island, between the two. They are numbered clockwise, in a circle. Click here for a map.
In general, expats tend to settle in the Buda side, as it is quieter, more residential and has more trees and gardens. One great area is District 2, as it is quiet, green and close to many public schools. Rozsadomb, or Rose Hill, is a prestigious neighborhood that is upscale and expensive. District 2 is close to the castle and has easy access to the Metro Line.
Another Buda neighborhood is District 11, called Újbuda, or “New Buda.” Technical University and ELTE University are here, so there are many students. Rich people used to live here before they moved to the hills, but it still remains upscale. Kelenfold is the crowded, urban area. Sashegy and Sasad are nice, residential areas, more far out from the city. Public transit is available, but it is much easier to live there if you have a car. District 11 is not as expensive as many of the other Buda neighborhoods.
District 12, the “Buda Hills,” is the place to live if you are into trees, hills and overall greenery. People even ski around here in the winter. There are a couple of bus lines in the area, and it has many wonderful views of the city.
In terms of the Pest side of the city, District 13, containing Újlipótváros and Angyalföld, is a great option. Though it is a downtown area, there is a nice balance of relaxing and stimulating in Újlipótváros. It is a clean, safe, pretty neighborhood with a nice park and riverside access. Angyalföld, or “Angel Land” is more working-class and farther from action.
District 14, Zuglo, is known to be quiet and full of family homes, but is not too far from any of the urban action in Pest. It has many options of public transit in the day time, but they shut down at night. It is not too expensive to dwell here, even if you have a family.
District 5, Belváros, is the most happening, downtown area, located right on the Danube in Pest. It is great for shopping, nightlife and access to resources, and is home to the Parliament buildings and many ministries. If you look, there are many unrenovated apartments that are cheaper, and you can buy them and fix them up. This area is inconsistent, as some apartments are very fancy while others are run down, and many are expensive.