I lived in BRU for 4.5 months back in 1998. The public transport there is great--they've got 3 metro lines and quite a few trolley lines & busses. I didn't have a car and didn't have a problem getting to where I needed to go. In particular, the Ren you're at appears to be about 5-6 blocks away from the Trone metro stop, just one stop south from where all three metro lines intersect, so you're in good shape there. As for the airport, public transportation does fall down a bit, as there are only a couple of busses that head out there. However, if you can get to any of the three main train stations (Gare du Midi [south], Gare Central, or Gare du Nord), there is a train from each of those stations directly to the airport, but I don't know what time they start at or how often they run.

Here's the website for BRU public transport (in French and Flemish; I'm not sure if they have an English version):

http://www.stib.irisnet.be/

Brussels is a great city...good luck & have fun!