The best place to visit on current dates and on the said duration is srinagar. The weather at that time would be very pleasant and you can visit many places around srinagar. One night stay in a houseboat is must. That's a really good experience
Coorg is a popular hill station located in Karnataka known for its flourishing flora and massive mountains. You can find Teak and Sandalwood trees scattered throughout the forests in Coorg. It is the home of exotic faunas like Dhole, Gaur, Asian Elephant and Wild Boar.
The chief attractions in Coorg are Abbey Falls, Namdroling Monastery, Nagarhole National Park and Talacauvery. Its a haven for nature enthusiasts and adventure freaks. Indulge in adventure sports like Fishing, Whitewater Rafting, Bird Watching and Paragliding.
Rejuvenate yourselves by taking a stroll across the aromatic coffee plantations. Visit any time between October and March which is the best time to see this place. Hotels in Coorg-https://www.ulohotels.com/coorg-hotels-and-resorts
Hey! During the month of May-June, Its good to visit places like Ladakh and Spiti (if you are looking for some real adventure and never seen before landscapes). In winters (Nov-Dec), you can witness the real Himalayan beauty at some offbeat places like Jibhi (Himachal Pradesh), Auli (Uttarakhand), Munsiyari (Uttarakhand), Shoghi (Himachal Pradesh) to name a few.