Not for only Goa, but 90% everywhere, this trick will help you to find cheapest hotels deals.
Book 1st night ticket online. After Reached there, search hotels locally.
you'll get the same 3 star hotels half in the price. I did it while I traveled in Kashmir, Shimla, Goa, Lakshadweep and Dharamshala.
I would recommend you to use TripAdvisor to looks for hotels in Goa as it's an aggregator which will compare the prices of hotels from various websites and offer you the cheapest price possible.