One of the places to watch the Boat Race is from one of the official fan zones. There are two official spots: The Hammersmith Fan park in Furnival Gardens and the Fulham Fan Park in Bishops Park. Both zones are open from 11am and have big screens showing the BBC coverage of the race, food stands, bars and, essentially, loos. Both are also dog friendly.
You're allowed to bring your own food and drink (booze included) too, as well as the all-important folding chairs if you don't want to get grass stains on your nice chinos.