Brussels International Airport, known locally as Zaventem, is a bustling hub, with direct flights from many U.S. cities. A cab ride from the airport to the city center will set you back upwards of €40 (about $50). To save euros, and time wasted in traffic, head to the train station in the airport’s basement. Direct trains to Brussels' three main stations leave every 20-40 minutes and cost about €8.
Brussels’ historic center is easily walkable, but to explore its other neighborhoods (something you really should do) you need to brave public transportation. The metro, trams, and buses all use the same ticketing system. You can ride anywhere within the system (including transfers) within an hour, for about €2. Buy a 10 "jump" ticket for €13.50 to save time and money.