If you are planning to take in some local sites around the Nurburgring there is the small town of Nurburg itself with its Castle on a hill above the town. The view across the Eiffel mountains from the castle is fantastic and you can see as far as Cologne on a clear day. The mountains are perhaps best enjoyed with a drive though and you could head south to Cologne, about 70 miles, or north west to Frankfurt.
Cologne is a city known for its Gothic Cathedral and it has a beautiful setting on the Rhine. There are also a large number of Museums and Art Galleries in Cologne. As for Frankfurt it is a more modern city and a major Financial centre for Germany and Europe. Apart from the Cathedral and the half-timbered houses of Romerburg Square there is little history to see in this city that dates from 794; Frankfurt is an example of how a city can be constructed to be modern and beautiful though.