Regions by Interest
India has 28 states and 8 union territories, demarcated broadly by spoken language. You cannot see it all in one trip. I haven't done it in a lifetime so far, even as an avid traveller. Pick by your interest instead:
Mountains and trekking
The Himalayan north: Jammu and Kashmir, Ladakh, Himachal Pradesh, Uttarakhand. Hill stations, high-altitude treks, many of the famous Himalayan pilgrimage sites. Kashmir is a honeymoon paradise with some great lesser-known treks. In the east, Sikkim offers high-altitude lakes, orchids, and treks both easy and hard. First-time trekker? Pick Pindari (easy, 6 days) in Uttarakhand or Sandakphu (easy, 6 days), with views of four of the world's five highest mountains. You want hard? Try the Goechala trek (10 to 12 days, hard) with views of Kanchenjunga, or the Markha Valley trek (6 to 8 days, moderate to hard) in Ladakh. Or more like a walk in the park near the Dalai Lama? The Triund trek (2 days, a breeze).
Beaches and islands
While people talk about Goa for beaches, some of the most pristine beaches are not there. I would say Marari beach in Kerala, Maravanthe in Karnataka and Gopalpur beach in Odisha. If you are into kitesurfing, the best spot in India is near Tuticorin in Tamil Nadu, very close to Sri Lanka on the other side. Havelock, the well-known dive island in the Andamans, Bangaram in Lakshadweep, Majuli (the world's largest river island) in Assam and St. Mary's Island in Karnataka are all worth your while.
Palaces, forts and heritage
Rajasthan: miles of desert, colorful palaces, enchanting forts and cities. Delhi, the capital, anchors the plains with centuries of layered history, and Agra's Taj Mahal is a short trip away. South India's historical temples (Tamil Nadu especially) are a heritage circuit of their own.
Spirituality
The Ganga and Yamuna plains hold Varanasi, Rishikesh and the great pilgrimage cities. The Jagannatha temple is in Puri, Odisha. The Char Dham Himalayan shrines draw the devout north. In the south, while Madurai is celebrated for its stunning gopurams, Tirupati and Sabarimala draw the largest crowds. Sringeri in Karnataka is the most important seat of Advaita Vedanta philosophy. Tiruvannamalai in Tamil Nadu is the spiritual center of Ramana Maharshi.
Nature, wildlife and the offbeat
The Northeast, reached via Assam: tea gardens, the Indian rhino, orchids and lower Himalayan treks in Arunachal, and tribal cultures across Manipur, Meghalaya, Mizoram, Nagaland, Tripura. Remote, less touristed, and best done with a tour operator. Tigers? Kabini in Karnataka, Ranthambore in Rajasthan and Tadoba in Maharashtra; you will nearly always see one or more if you spend 2 nights. If you are into lions, it's Gir in Gujarat. Elephants abound in the Karnataka, Kerala and Tamil Nadu forests, especially the Mudumalai, Bandipur, Nagarhole and Wayanad wildlife sanctuaries: together the largest continuous forest in the south. The easiest place to spot the snow leopard (a very, very elusive one) is Hemis National Park in Ladakh, and Pin Valley National Park.
Offbeat places include India's longest drivable beach (Muzhappilangad, Kannur, Kerala, about 4 km), the Patal Bhuvaneshwar cave temple in Uttarakhand, the Yana limestone caves in Karnataka and Menchuka in Arunachal Pradesh.
Cities
Mumbai (formerly Bombay), home of Bollywood. Delhi for history and food. Kolkata (formerly Calcutta), the east's biggest city. Bangalore, the now messy, traffic-ridden Silicon Valley of India, which used to be the pensioner's paradise.
Beyond India
Popular destinations nearby: Sri Lanka, Maldives, Nepal and Bhutan.