Varca , Cavellossim , Benaulim , Palolem , Agonda are all great beaches in south goa.
You can travel to dudhsagar falls and devils canyon. If you feel like going to a church then there's bascillica of bom jesus. For Hostels try Hostelworld app or the website. Happy Travelling ! :)
Why do you want to stay in south goa? North goa is the best place to live in. Most of the amazing beaches are in north goa and you will have to travel at least 30-45 min every day from south goa to north goa. There is beach shack in north goa at Mandrem beach which is not so costly and you get a place to stay by beach side. Look for Molly's Nest, Mandrem Beach.
I love South Goa!! Agonda is my favourite beach, its beautifull, has the perfect sunsets, the crowd is amazing in agonda and it`s a peaceful place. The best in whole of Goa if you ask me. Also, there is a place called Jojo lapa in Agonda, it,s right on the beach i always love having a meal there, during sunrise and sunsets. i highly recommend it.
Places: Grande Island for scuba and dolphin tour, dudhsagar waterfall trek, Goa Karting in Nuvem, watersports at Mobor Beach, agonda, cabo derama, palolem, galgibaga beach are good, butterfly beach. Salaulim dam, netravalli wildlife sanctuary etc.
My suggestion is book ur hotel in panjim n not in South Goa as panjim is d centre most place... n dhudsagar treking in South Goa, Vasco port harbour n airoplane museum... in panjim n near Baga,calungate, condolium, vagartor,fort n beach,reies mangos,berqulium, Dona Paula, mapusa. mny