Yes. Germany's US State Department rating is Level 2 ("exercise
increased caution") — the same as France, Italy, the UK, and most of
Western Europe — and that level reflects the generic European
terrorism advisory rather than anything specific to Aachen.
Aachen itself is a quiet, mid-sized university city; violent crime
against travelers is genuinely rare, and police presence is visible
around the cathedral and the main train station.
On a Passports teacher-led trip, the group is never on public
transport alone, the Tour Director runs a first-evening awareness
briefing covering the handful of pickpocket-prone spots (the main
station, Karlsfest crowds, the Christmas market), and every hotel is
pre-vetted for 24-hour reception and secure room storage. We operate
a 24/7 emergency line out of Boston, keep parents on a daily-update
channel, and have English-speaking medical contacts in the city. For
most teachers running their first school group tour of Germany, the
logistics feel easier than a domestic field trip.