If it's your first time solo then start with an easy one. Rishikesh would be an ideal choice for it. Stay in hostels-they have female dorms as well. You can spend 2-4 days there which will cost you around ₹2500-3000(everything included). Enjoy morning at Ganga beaches there. Other attractions are- Beatles Ashram, Laxman Jhula, Ram Jhula,Shivpuri rafting, Evening Arti at Triveni Ghat. All the best!