The Bursa City Museum (Bursa Kent Müzesi) occupies the restored Ottoman-era municipal building on Atatürk Caddesi, a short walk from the Grand Mosque. The museum covers the history of the city from prehistoric times through the Ottoman period and into the 20th century, with particular emphasis on Bursa's role as the first Ottoman capital and its importance in the silk trade.
The exhibits are well presented with good English labelling, and the building itself — with its late 19th-century Orientalist-Ottoman revival facade — is worth a look. There is a good section on traditional Bursa crafts: silk weaving, karagöz shadow puppetry (which originated in Bursa according to local tradition), and chestnut production. The Karagöz and Hacivat Museum is nearby for those interested in the folk theatre tradition.