If you want to explore mountains, so you can visit 1. Darjeeling ( April to June & October to January)
2. Kodaikanal , tamilnadu ( October to July)
3. kasol ( Throughout the year)
4. Nainital ( March to June & October to February)
5. Lonavala, Maharashtra ( October to may & June to August)
With summer on the process I will share a few budget hill station spots of India, Kausani Uttarkhand Chakrata uttarkhand
Kasauli Himachal
Kasol Himachal
Yelagiri Yercaud Tamilnadu Wayanad Kerala
Aizawl Mizoram