Harrow is straightforward to reach from central London by Underground. Harrow-on-the-Hill station is served by the Metropolitan line (Zone 5), and fast trains from Baker Street take around 25 minutes. The station sits at the foot of the hill, from which the village and school are a steep ten-minute walk. Harrow & Wealdstone station (a short walk away) is served by both the Bakerloo line and the London Overground Lioness line, offering additional connections.
There is no reason to drive. Parking is limited, the streets on the hill are narrow, and the Metropolitan line from Baker Street is frequent and direct. If you are coming from north or west London, a combination of Overground and Metropolitan connections works well — check Transport for London's journey planner for the best route from your starting point.