Hi Lana and welcome to EasyExpat.com

As a start, I recommend you to read our guide for expatriates in Brussels where you will find information on accommodation.
Nice (and expensive) areas include:
- close to the centre:
Ixelles (many international and European schools), Saint-Gilles (close to Charleroi), Etterbeek, square Marie-Louise, Schaerbeek (towards Jamblinnes de Meux square), Sablons, Notre Dame aux Neiges.
website for Ixelles: http://www.elsene.irisnet.be/

- further out (some don't have access to the metro) :
Uccle, Woluwe-Saint-Lambert, Woluwe-Saint-Pierre, Auderghem, Watermael-Boisfort.
A lot of expats live in expensive areas in the south (Uccle and Ixelles):
Uccle: http://www.ukkel.be/

The main area for the European Union offices is around the Léopold district (rue de la Loi/ Robert-Schuman roundabout). Mostly offices it's not really an area to live in but you can go near Place Boniface.

Saint-Antoine (Forest), Aumale (Anderlecht), Molenbeek have recorded some issues with violence, riots and cars put on fire. Anneessens is very poor.