I believe you can apply for a Tourist visa. If you can show enough funds for the visit and the detailed travel plan ,depending on your circumstances they might issue even without a visa from a friend or a relative. They have to satisfy that you are a genuine tourist and will return back.
If you have enough money, no need of sponsor letter stuff. But having an invitation letter increases your chances of getting visa.
Unlike Sri Lanka, tickets tourist attractions cost between Rs. 5000.00 10000.00+, so its gonna cost u a pretty penny.