Aachen sits on the border with Belgium and the Netherlands and is home to RWTH Aachen, one of Europe's top engineering universities. Very international, very student-heavy, and affordable.
Arriving in Aachen: you must register your address (Anmeldung) at the local Meldebehörde within two weeks of moving in — that is a legal deadline under § 17 Bundesmeldegesetz, not a guideline, and missing it carries a fine of up to €1,000. Budget roughly €450/month for a WG room, though see the caveat on that figure below.
Deadline and fine: § 17 BMG, § 54 Abs. 3 BMG.
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