The Santa Monica History Museum on 7th Street covers the city's development from the Tongva people who lived in the area for thousands of years through the Spanish mission period, the late-19th-century beach resort era, and the 20th-century growth of the city. The museum is small and the exhibitions are well curated rather than exhaustive — you can cover it in an hour.
Particularly interesting are the exhibits on the 1920s and 30s, when Santa Monica was a Hollywood satellite city and the beach front was home to estates like the Marion Davies compound. The Tongva collection is also worth time — the museum treats the history of the indigenous people of the basin with more depth than most local history museums in the region.