Uttarakhand is the best option for a solo travel. Rishikesh in uttarakhand is the right place for a week travel. You can start you day with yoga session and end it with the holy ganga aarti. You can try out adventure activities like bungee jumping,giant swing, flying fox, etc. For budget travel stay at a hostel instead of a hotel. You'll get to meet more people and you can as well travel with them.
If you have a week in your pocket, I would suggest you to go and explore spiti.. The time is also perfect.. you can either go via Manali or you can take a round trip covering Shimla reckong pio, spiti and Manali.. Have a great travel ahead..
If you want to be in cold places in summers to refresh yourself from the summer then I would suggest you to visit uttarakhand, himachal pradesh or kashmir during this time. some of the best places includes spiti, McLeodgunj, triund, kasol, leh and many more.
Ho Sourabh, May will be summer in India. So you can go to the following places: Kausani, Chail, Spiti, Bir Billing, Kerala, Mclodegunj, Lansdowne, Tawang, Shillong, Sandakphu, Dandeli, Horsley Hills, Kadmat Islands.
Hyderabad is the best place
you can visit charminar,golconda and many more
since you are visiting in summer u can go to resorts in hyderabad
There are many resorts like hidden castle,wonderla,leonia and many more