You can start with either Rajasthan or Himachal Pradesh. You will come across a number of domestic as well as foreign solo as well as group travellers in both the above places and also there are plenty of hostels to stay, meet and mingle with like minded travellers.
If you want to go for a solo trek, please try Kumaraparvatha trek. If you are obsessed with architecture kind of place, please visit Hampi or Pondicherry. If you love beaches, visit Gokarna.