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.