Hello Priyanka, You can try Cabo de rama and Palolem in south goa. Both offer nice less crowded beaches. You can contact Seldon Fernandis for accomodation options. He has whole range of options to choose from. #: 7507648918 Hope this helps.
Hey Priyanka, South Goa is just perfect for those who want to avoid the crowded places in Goa. One of the best way to explore South Goa is by renting a bike and head out to beaches like untouched Palolem beach and Majorda beach. Trek to Tambdi Surla waterfall, rock climbing in Netravali wildlife sanctuary and Rivona caves.
Pretty much agree with the other folks, but South Goa will be pretty much closed in the end of September. They start opening only from October 1st week or 2nd week onwards. For me Goa is only about South Goa and I have been going there for over a decade and will be there again in the second week of October only because everything will be shut in September. But no harm in finding out.