On the Parade Route
The Guard Mount marches up Sheet Street, wheeling left into the High Street, past the Parish Church and the Guildhall, then turning right onto Castle Hill by Queen Victoria's Statue and up Castle Hill into Windsor Castle. The best places to see them are on Windsor High Street or on the Corn Exchange under Windsor Guildhall.
Inside Windsor Castle
Standing by the railings, just below St George's Chapel, will give you a good view of the ceremony. When the monarch is in residence, the ceremony takes place in the Upper Ward, on the lawn of the Quadrangle. Standing next to St George's Gate, inside the Castle, will let you see the Guards and Band march right past you, close enough to touch. From the railings at Engine Court, you can see the entire ceremony with The King's Private Residence providing a spectacular backdrop.
From time to time, other areas, including the Moat Path, are opened to let visitors watch the ceremony. The friendly uniformed Wardens will guide you to these when available.