You can Andaman Nicobar island as your perfect solo trip destination . Here you can visit Havelock island.Andaman is famous for beaches . It is known as Kalapani .Andaman is blessed with perfect landscape,sunkissed beaches,clear blue water makes andaman unique from other destination . You can do scuba diving,snorkeling,beach bumping,sight seeing ,bird watching,kayaking and you also get variety of sea foods.If you are looking for cost effective tour you can choose andaman as your perfect destination without any doubt.Other places you can visit are Govindnagar beach,Elephant Beach,radhanagar beach etc.
There are many good suggestions on this for where to go. But i think you should go solo with a group once. Group travels are a bridge between travelling with someone known and travelling all solo. You will have around 10-15 strangers in a group and you will get to meet new people too. This was a suggestion from one of my friend for my first solo trip to Tirthan valley and i am glad i listened to my friend and went on that trip with 15 complete strangers because that was one hell of a memorable trip.