If you are considering moving to Finland it may be difficult to useful to know something about the most popula living areas in Finland. They are presented in order of popularity and it correlates with the price:-)
Eira, Kaivopuisto and Ullanlinna
This is area at the southern Helsinki is a living area between the city center and the Baltic Sea. It is very nice living area and from this area you can walk to the center or take a tram. Buildings of this area are usually from the early 1900 but most of them are renovated and in good condition. This area is rather peaceful and safe place and services are good, small shops and grocery stores are very close and big department stores at city center are easy to access.
Westend and Kulosaari
If you want more space around you and prefer bigger houses, Westend is the best place for you. Westend is a small luxorious area by the sea few kilometres from the Helsinki center to the west. There is a bus connection from Westend to the center but a car is strongly recommended if you stay here.
Kulosaari is another similar area with big luxorious houses. Difference to the center is longer but there is a metro connection so it is actually better if you don't have a car.
Punavuori and Kamppi
Punavuori and Kamppi are areas very close to the center and slightly norther than Eira, Kaivopuisto and Ullanlinna. The difference to this first area is that in Punavuori and Kamppi you are closer to the center but area is not that peacuful, there are more bars and nightlife, which may cause some noise during nighttime. If you don't mind that this area is a good choice. Price level is slighlty cheaper and at this area there are more small appartments available (1-2 rooms+kitchen). Perfect place for young adults without children.
Katajanokka, Kruuununhaka and Etu-Töölö
All appreciated, peaceful and safe living areas close to the center. Price level slighlty cheaper than in Eira, Ullanlinna and Kaivopuisto area. If your budget is not unlimited but you want to live in nice area these are very good options. There is still a walking distance to the center.
Lauttasaari, Taka-Töölö and Meilahti
Lauttasaari is an island at western Helsinki. There is a bus connection (appr. 15 minutes) to the center. This area is very popular among young families. There are basic services at this area and distance to the center is not too long.
Taka-Töölö and Meilahti are areas on northern side of the center. Difference to Lauttasaari is that this area has slighlty better public transport connection because there is a tram line. There are some streets where traffic can be noisy but in general this is also a good area to live. If you want to avoid noice don't rent an appartment at Mannerheimintie, Mechelininkatu or Tukholmankatu because they are the busiest streets.
Kallio, Alppila and Hakaniemi
This is an area not far from the center. This area has many bars and nightlife activities but it is popular among young adults without children. Sörnäinen is very similar area but distance to the center is longer.
Munkkiniemi is a nice area from north-west to the center by the sea. There is a tram conncetion to the center (appr. 20-30 minutes). Peaceful area and especially at summertime it's beautiful.
Herttoniemenranta and Aurinkolahti
If you prefer new appartments these can be your choices as well. They are both new areas at eastern Helsinki by the sea. From Herttoniemenranta it takes appr. 15 to get by metro to the center and from Aurinkolahti it takes much more appr. 25-30 minutes.