Route 66 used to end near the Santa Monica Pier. You can still visit its classic merry-go-round (which was featured in The Sting.)
Though not precisely a Route 66 attraction, you might be interested in the Petersen Automotive Museum on Wilshire Blvd. near Fairfax (about 10 miles east of Santa Monica). Classic cars are featured in "historic" settings, and there are also exhibits on Cars of the Stars, etc.