Enjoy your visit to my dear old hometown! You may want to have a look at my travel pages over on Virtualtourist, here is the one on Braunschweig:
http://members.virtualtourist.com/m/f86bd/11bf7/
Goslar:
http://members.virtualtourist.com/m/f86bd/eb1b/ is an excellent recommendation for a day trip.
There is another pretty and small old town much closer to Braunschweig that I'd like to mention, and that's Wolfenbüttel:
http://members.virtualtourist.com/m/f86bd/17dd/ This can be done as an afternoon or even quick evening visit. Take the bus No. 420 from Rathaus and you are there in some 20-25 minutes.
You will find quite a number of student pubs and cafes in all varieties around the central university campus. And the city's best-known pub mile is Magni quarter, a preserved old quarter in the Southeast of the city centre behind Kaufhof department store (which is impossible to overlook).
And the tram is indeed the M1, there are no S lines in Braunschweig. The M1 also continues to the university area.