Mahabaleshwar, Matheran, Lonavala in Maharashtra
Valley of Flowers in Uttarakhand would be the best. In Kerala - Alleppey, Munnar, Wayanad. Shillong and Cherrapunji in Meghalaya.
Also Coorg and Kodaikanal.
Kerala would be a beautiful place to.visit during the monsoon. it won't be too cold, not will it be too hot. it's a right mix and plus you can really enjoy the rain amongst the great food and a few indoors