New in Tallinn

City24.ee and kv.ee have the most information on renting flats.

On city 24, you can put in the parts of the city you'd like to live in.  Here's some info:
Old Town (Vanalinn) is right in the center of the center where the tourists go.  This is where I live.
Kesklinn is the city center
Kristiine is still the city center but a bit farther from Old Town
Kadriorg is mostly houses and families
Lasnamäe and Mustamäe are mostly Soviet Era 5 - 8 story gray non-descript row after row after row of apartment buildings
Haabersti is newer housing and apartments, a bit farther from the city center close to water (but water is everywhere in Tallinn)
Pirita is the beach area of town--more expensive than most other areas other than Old Town
I'd stay away from Põhja-Tallinn and I don't know anything about Nõmme.

Feel free to message me or email me at [email protected] if you need assistance.  I only work on Wednesdays, and would have plenty of time to help you orientate yourself to Tallinn.  There is also a possibility that my flatmate will be going to work in the US for several weeks in February.  If that is the case, I may be able to temporarily house you in my flat while he's gone.

Allen