The Museum-flat of Andrey Sakharov is a small but pointed stop, tied to the years when the Nobel Peace Prize-winning physicist and human-rights advocate was exiled in what was then Gorky. It is not a grand museum; the power is in the domestic scale and the political context.
Visit after seeing the kremlin and the old merchant streets, when you want a more recent layer of Nizhny Novgorod history. English interpretation may be limited, so reading a little about Sakharov beforehand makes the rooms much more meaningful.