There is the old towpath,now a public road for pedestrians, that runs, with some interruptions for buildings, from Hammersmith Bridge to Bishop's Park. I used to have a flat which overlooked the river at Holyport Road roughly half -way down. On boat race days, the towpath was comparatively quiet, mainly because it is not obvious to outsiders and locals either had a view from their own flats or couldn't be bothered to go down ( or were all in the Crabtree pub, a short way from the flats, the garden of which also gives on to the river! The pub has been tarted up as a gastro pub now and is likely to require bookings and be crowded anyway) . Find this all in an A-Z. Look for Fulham Place Road; the path is to the left of the map, down several of the streets off it.
It is pleasant to be present, once in your life, at historic or important sporting events. True, this one is a bit 'blink and you miss it', because the flotilla and boats only take a few minutes to travel that whole stretch.