Take a student discount bus or train from Enschede to Koblenz, the closest major city to Nurburgring. Buses such as Flixbus often have low rates, especially if booked in advance.
Wander through Cologne's Old Town to experience its historical charm with colorful buildings and local boutiques. This is also a great area for souvenir shopping.
Enjoy some traditional German cuisine for dinner at Brauhaus Putz. Their range of beer and local dishes provides a great student-friendly dining experience.