The former governor’s house inside the kremlin is now the Nizhegorodsky State Art Museum. Exhibits range from 14th-century icons to 20th-century paintings by artists such as Nikolai Rerikh and Vasily Surikov.
The museum begins (on the left after you enter) with 14th-century icons. The entire collection is chronological, so you can see by room 6 how rudimentary landscape perspectives creep into 17th-century icons. After the icons comes the large collection of mostly oil-on-canvas paintings by Russian masters, culminating in Soviet art. The English descriptions are excellent.