Most of the places that you can do by road/rail in 3 days are going to be really warm in these months. You are better off with a hillstation during this time try the below 1. Meghamalai ( Theni District )
2. Valparai (Coimbatore District )
3. Kodaikanal and around
4. The smaller hillstations - Yercaud, Yelagiri or Kolli - they might feel a little underwhelming given what you may have been used in Kerala already.
You could visit Karnataka - Coorg, Chikmagalur, kudremukh are popular spots besides Bangalore and Mysore. Maharashtra- Mahabaleshwar, Panchgani, Matheran, Igatpuri are some spots besides mumbai and Pune. Himachal- Manali, Shimla, Uttarakhand- Nainital, Mussoorie, Auli, Chopta besides Dehradun. Tamilnadu - Ooty, Kodaikanal, Yercaud, Coonoor besides Madurai, Coimbatore and Topslip. There are some authentic spots to visit in North east India like Tawang, Darjeeling, Sikkim, Imphal and Mizoram.
Goa is one of the most favorite destination among Indian tourists due to its pristine beaches. Dotted with hundreds of impressive beaches in Goa, the incredible coastline of more than 100 km offers beautiful views and serenity where tourists enjoy and relax in.