I would say Goa . I know people are going to laugh at this... But Goa is beautiful and surreal during the Monsoons. Not too expensive , the weather is really pleasant and its extremely safe ....Having said that yes most of the shacks are closed , most of the time there is high tide. But its definitely better than visiting during the summers. Just came back last week and would recommend everyone to visit during the monsoons atleast once. Its a different kind of beauty !!!
Places near to Pune or Mumbai like matheran, lonavala, mahabaleshwar are must visit during monsoons. Also there are many trekking spots and waterfalls near Pune/Mumbai. Monsoons add more charm to Munnar, Kerala.