Into the Harz
When I was in Potsdam , I told the landlady that I intended to go to Goslar. "Ah, wandern in Die Harz" she replied. No, I said, that would be too much like hard work. But that's just what I ended up doing. I took the bus up to Hahnenklee, a small village and ski resort up in the mountains (as mountains go, the Harz are admittedly not exactly the Alps). It's a winding vertiginous trip, most notable on the way back down. The village is quite charming, though marred by the brutalist concrete ski accomodation. I took the cablecar up and wandered through the forest back down to the village. It would be relatively easy to walk right back to Goslar if you wished. It was a fine late September day and the air was almost supernaturally clean and fresh. It was an incredible contrast to the mayhem of T'wiesen (Oktoberfest) where I had just been, and Berlin where I was previously. If you wish to stay in the village, there is a fair range of accomodation, and even a bus direct to Berlin.
The market church of Cosmas and Damian is distinctive due to it's different spires.
The first mention of a church on this site was in 1151.
I didn't get a chance to go in but it's a fantastic building from the outside.
Vestibule of Church of St. Simon and Judas
Only the vestibule (Domvorhalle) of the Collegiate Church of St. Simon and Judas (Stiftskirche St. Simon und Judas) remained till our days. The church itself was built in 1047 simultaneously with the Imperial palace. The vestibule itself was built a century later in 1151. The church was used as a model of many Romanesque churches all around Germany. It also had a big influence in the church politics.
The church was demolished in 1820.
Here you may see the plans how the church looked like: http://www.pe.tu-clausthal.de/agbalck/dom/dom-poster.pdf and plans for the reconstruction.
World Heritage mountain city
Goslar is a Unesco World Heritage site and yet so unknown to non-Germans it's amazing! My guess is that is has always been too close to the old DDR border for westerners to bother with and they've gone to Bavaria and the Black Forest instead when they've wanted mountains. The one exception is probably coach loads of Swedes in spring as Sweden is close to northern Germany. I am priviliged as I can return to this gem now and again, having family in nearby Wolfsburg (and there you need to get away and feast your eyes on gorgeous architecture sometimes!). Since the reunification of Germany, more people come here but it is also now competing with the picturesque former GDR town of Wernigerode on the other side of Mount Brocken. Go to both and decide which one to favour in future as I'm sure you will want to return to the Harz mountains.