National Galleries of Scotland: National, The Mound, Edinburgh

The National Gallery showcases a huge variety of art historical artworks, both Scottish and international. Admission is free. Family-friendly features include a buggy park (requires a coin to operate, similar to a swimming pool locker), baby changing facilities, and regular exhibitions aimed at children. There are no dedicated breastfeeding facilities, but staff told me that they would be happy to open up a room in the education area on the first floor if it was not in use. The venue also runs free, drop-in Family Fridays during term time; see their website for the most up-to-date information.