Across from the castle on the main high street is a hotel and beside it an archway - drive through the archway and one comes to a carpark (not free).
It does get rather busy though.
The other alternative is - as one enters the town from the M4 - there are 2 car parks (near the river) - Pay & Display - from here it is only a 5 minute walk up to the castle.
What Richagadir said
There is a car park next to Browns (hidden behind it) and also one next to the Windsor Royal Theatre
Also one in Windsor Home Park (5 min walk) and single yellow line and P&Display parking along the river
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