You must note that most Indian embassies and consulates won't issue a visa to enter India unless you hold an onward ticket, which is taken as sufficient evidence that you propose to leave the country.
A special People of Indian Origin (PIO) card are also available only to people of Indian origin (excluding those living in Pakistan and Bangladesh) who hold a non-Indian passport ie. NRI’s and live abroad (maximum fourth generation). The card costs around $570 and offers multiple 15 years validity entry from the date of issue. Person of Indian origin can also obtain five-year multiple-entry visa which costs around $240.
Visa ExtensionsYou can get max fifteen days visa extensions only under extraordinary circumstances (by no means as a matter of routine) from Foreigners' Regional Registration Offices in the main Indian cities. You can only avail another six-month tourist’s visa by leaving the country.
Restricted Area PermitsEven with a valid visa you’re not allowed to travel everywhere in India. Certain places require special extra permits.
Andaman Islands: Foreigners need a special permit to visit the Andaman Islands. The Nicobar Islands are off limits to all excluding Indian nationals employed in research, government business or trade.
Himachal Pradesh & Uttaranchal: Special request are required to enter some areas close to the India -- Tibet border in Himachal Pradesh and Uttaranchal. For the crossing Iron Kinnaur to Spiti in Himachal Pradesh, tourists must obtain an inner-line permit, which is free.
The Milam glacier in northern Kumaon in Uttaranchal, which also falls into Indo-Tibetan Border Authority jurisdiction, is presently is also thrown open to travelers at the discretion of the local police.
Karnataka: All foreigners are legally permitted to obtain a Protected Area Permit (PAP) before making a tour to the Tibetan settlements between Hunsur and Madikeri. These can be obtained through the Ministry of Home Affairs in New Delhi.
However it can take several months for the paperwork to go through, so it's better to enquire with a Tibetan office or organization in your home country, as permits can sometimes be arranged from abroad.
Ladakh: You'll require a special permission for going up to Khardung La, as well as for crossing down into the Nubra Valley. Valid permissions are also required for visiting Pangong Tso, Tso Moriri and the Dha Hanu Valley.
Lakshadweep: All visitors need a special permission if you are making a visit Lakshadweep. Both foreigners and Indians can stay on Bangaram, Agatti and Kadmat. Indian citizens can make day visits to Kalpeni, Minicoy and Kavaratti.
Northeast States: No permits are currently allowed to visit Assam, Tripura or Meghalaya, although you may require to register with the police on arrival at airports in the region. Entrance to Arunachal Pradesh, Nagaland, Manipur and Mizoram can be bit difficult to obtain. Nagaland is currently the easiest state to enter, but it's best to book through a travel agent in the northeast. Arunachal Pradesh permits cost US$50 per entry.
Rajasthan: Special permission is required from the Collector’s office if you’re visiting Jaisalmer due to its close proximity to Pakistan border. Permission is only issued in special circumstances. The only regions exempted are Amar Sagar, Bada Bagh, Lodhruva, Kuldhara, Aka Sam, Ramkund, Khuri and Mool Sagar.
Sikkim: If you are visiting Sikkim you need to require a 15-day permit. These are free and easy to obtain.
West Bengal: Foreigners need a permit (free of charge) for making a tour to Sunderbans Wildlife Sanctuary. These are issued on the spot (on presentation of your passport) at the West Bengal Tourism Centre in Kolkata.