If you are a student in the RWTH, you can ask the "Sprachenzentrum" in the University. They might have some free English courses. I am not sure if they have trainings for IELTS. They are in Karman auditorium: http://www.sz.rwth-aachen.de/Ww/Kontakt.html You can either visit them or write an email.
Except for VHS, another place you can ask is Spr@achen. But you will have to pay there for sure. http://www.spraachen.net/
Telefon: +49 (0)241 - 39 999
Fax: +49 (0)241 - 40 76 41
E-Mail: mail@spraachen.de (an Beratung K9)
Augustinergasse 8, 52062 Aachen
It seems the nearest test center for IELTS is in Cologne. I don't know if some language trainers take care of the registration for the exam.
