There are five administrative districts, each one further divided into particular city parts.
See the map here
Bratislava I - Old Town
This is the central district, also called Staré Mesto - The Old Town. With its location and the historical center it is the most popular district to seek 
accommodation, job and entertainment. It is the smallest out of five districts. It spreads out on the left bank of Danube and offers a lovely walk around the historical pedestrian zone Korzo and other sights, like the Castle with a great view of the city, churches and small palaces, the Slovak National Theatre and number of charming little streets preserving some of the old Bratislava´s atmosphere. Not to be missed is the memorial Slavín towering above the city. Get in touch with nature in the original and untouched city park Horský Park or visit the modern shopping mall Eurovea with a buzzing park at the river, children´s playground and a variety of bars and restaurants.
The neighborhoods such as Palisady, Horsky Park and Castle hill with their historical apartment buildings and high ceilings are very popular residential areas. This location is sought also by international institutions, such as embassies and international schools. Property is relatively expensive in comparison to other districts but its central location and quality of housing make it a convenient place to live. Parking, however can, be a problem.
Bratislava II - Ružinov
It is the fastest-growing residential area of the city. It contains many new apartments, development projects and business centers. This district offers good rental opportunities. It stretches out from Ruzinov which is rather close to the center, to Vrakuňa and Podunajské Biskupice being the outskirts of the city. The Bratislava airport is located here. In Ružinov there is one of the three biggest hospitals in the city. Among the highlights are the biggest farmers´ market Miletička, the National Tennis center Aegon Arena, the artificial lake Štrkovec with a recreational and children-friendly area and a popular summer spot Zlaté Piesky with a lake, beach and a summer sports´ center Wakelake. More residential areas in BA II - Rozadol, Trávniky, Ostredky...
Bratislava III - Nové mesto
The district is located in the north and offers both modern apartments and larger family homes. This area includes also suburban living stretching to the Small Carpathians mountain range,
where local population likes going hiking. Popular neighborhoods are Kramáre and Koliba. Both offer good location only a couple of minutes by bus from the center, Koliba being rather more expensive with its big and exclusive houses. The woods of Kamzík and Železná Studnička interconnected by a cableway is a popular weekend spot for families with children, dog walking, hiking and outdoor sports. The neighborhoods of Rača and Vajnory lay on the edge of the city and are popular mainly for their vineyards and traditional seasonal festivals.
Nové Mesto is an extension of the city center and there are numerous business centers and shopping malls, among them the oldest mall Polus, which stands next to the leisure area Kuchajda. There is the Ondrej Nepela stadium where the Ice Hockey World Championship in 2011 was held. The arena and the Hant arena Pasienky are cultural centers holding all kinds of sports events, shows and concerts.
Bratislava IV
This district consists of Karlova Ves, Dúbravka, Devín, Devínska Nová Ves, Lamač and Záhorská Bystrica. Devínska Nová Ves and Záhorská Bystrica are on the outskirts. Karlova Ves is the closes
t to the center and with modern projects and apartment buildings it is a convenient residential area. Most of the student residencies are located here as well as The Cambridge International School, The British International School and the QSI international school. There is the ZOO and the Botanical garden and the modern leisure area River Park at the Danube. If you feel like making a day trip out of the city, focus on Devín and Devínska Nová Ves. Besides the lovely rural Devín´s feeling you will have a chance to step back in time by visiting the Devín castle. The historical ruins tower on a cliff above the rivers Danube and Morava and offer a panorama with Austria on the other bank. Extend your trip to Devínska Kobyla, the highest point of Bratislava valuable for its rich natural diversity and the paleontological spot Sandberg.
Bratislava V
This largest district 
is made of four parts, Petržalka, Jarovce, Rusovce and Čunovo. The last three are on the outskirts and offer nice family housing. As for culture there are historical sights and free-time activities, e.g. the ruins of the Roman military camp Gerulata, the Rusovce mansion, the Modern Art Museum Danubiana and the Water Sports Center Divoká Voda.
The biggest part of this district is Petržalka. It is known for multiple tall concrete apartment blocks, traces of the communist era. But Petržalka´s face has been changing significantly. It is a city inside a city. The residential potential is varied, from older apartments to new, modern projects, some of them right at the bank of Danube with a perfect view of the historical center. There are several important institutions, such as Incheba Expo Center, Digital Park Business Center, the French International School and a large Shopping Center Aupark. Next to Aupark there is Sad Janka Krála, one of the oldest parks in Europe, which is a popular leisure area with a riverside beach in summer and lovely boat restaurants and bars.