Another option would be to take the 2 line toward Clemenceau, as there is a stop right at Gare du Midi (i.e. no need to transfer to the tram like going to Gare du Nord), and as I recall, it's not a long walk from the station to the trains. Just don't go outside...the train station is fine, but the neighborhood is not (at least it wasn't when I was there in 1998). As for which train station that goes to the airport is closest to your hotel, I think Gare du Midi is your best bet, but I'm not familiar with the 12--it sounds like it's definitely worth looking into.

Addendum: I just found the train schedule for Brussels <-> airport:

http://ari.b-holding.be/root2/folder...11/Z010215.pdf

Look on pp. 83-89 of the PDF file (pp. 82-88 of the printed document).

The train is super-convienent; it drops you off at the bottom level of the airport. Simply take the elevator up 3 or 4 floors (I forget, but it's signed), and you're at the ticket counters!