The Fembohaus is a beautiful and palatial house in the Nuremberg Old Town which currently serves as the city museum. You'll come across it if you walk from the Hauptmarkt up to the Castle. The museum has good, free audiovisual media to guide you through the history of the city, the old house itself, and the lives of its former inhabitants. Strongly recommended for its beauty and its history.
It's funny and almost shocking to find a building like this in such a monumental and historic city, and that might be why it goes unnoticed by most visitors. The Neues Museum's architecture is interesting by itself, but it's also nice to find modern and contemporary art in such a historic setting. If the building wasn't so slim, I'm sure more visitors and works could fit, but I'd still totally recommend a visit.
Nuremberg is considered one of the great Toy capitals, and faithful to it's popularity offers the possibility of visiting the 'Spielzeugmuseum', or toy museum. This is one of the most impressive museums in Europe with a very extensive collection, and quality in each of the exhibits. It opened in 1974, and offers collections of all ages and ethnicities, especially the last 200 years. Its possible to find model railways, cardboard horses, and all kinds of toys.