Singaraja on the north coast of Bali has a museum called Gedong Kirtya that houses some interesting historical pieces. The main item of interest is the collection of lontar manuscripts. These are engraving of religious texts on the leaves of the lontar palm, like the ones found at the Bali Aga village of Tenganan.
Gedong Kirtya is the only museum of lontar manuscripts in the world and houses 3,000 or more separate pieces written in Old Javanese, Balinese and Indonesia, covering subjects such as folk history, black magic and astrology.
Gedong Kirtya also houses a set of inscribed bronze plates from the 10th century. These are called prasasti and are considered to be the oldest written records in Bali. Gedong Kirtya is located at Jl. Veteran #20 and is open Mon-Thurs 7am-2.30pm, Fri 7am-noon and Sat 7am-1pm.
You can give a donation upon entering and in my experience it is best not to wait till the end of the day to visit museums in Bali. The staff often try to close 45 minutes early, and then ask for money to open it just for you.