Weimar is a pretty town (and also has an element of a second WHS - Bauhaus - which makes it doubly as interesting).
There are quite a few places within the town that are part of this WHS. There were two that were my favourites. The first is the House of Goethe, where I thought they had done an excellent job of presenting the atmosphere of the house during his time, combined with a great modern museum.
The second place was the Wittumspalais which has a real sense of grandeur. It is a pleasure to explore and I spent a lot longer in there than I expected.