I used to be a regular visitor to the HSB when I was working in Europe. Don and Urias provide good advice. With only a day and a half Drei Annen Hohne is definitely the place to go. Take a roundtrip to the top of Brocken early the morning and hope for a clear day. I like the hike from DAH toward Wernigerode, you come to a sweeping curve and past it the only tunnel on the line. The station at DAH also offers some excellent photo ops. While the side by side departure from Alexisbad is no longer regularly scheduled, I keep seeing new photographs, so special trains must be common. You might want to check that, and maybe you will be lucky. The roads are good so you can get around fairly quickly. Look forward to seeing you pix.
JBWX