I'm Indian, so I'll add a few, particularly about some areas that are likely to be less well known to foreigners who may mainly have read or been told about the most popular tourist areas, such as the Golden Triangle (Delhi/Agra/Rajasthan), Goa and Kerala:
Go to parts of central India, e.g. Madhya Pradesh (MP).
https://en.wikipedia.org/wiki/Madhya_Pradesh
It's a big state. Lived there for some years. Apart from the usual touristic areas, of which there are some, try to check out the central Indian deciduous forests, comprising sal, teak, and many other species. (India has huge biodiversity.) I really enjoyed the many hikes I did in those forests.
Kanha National Park.
https://en.wikipedia.org/wiki/Kanha_National_Park
It has those deciduous forests I mentioned, with fauna that include tigers, gaur (Indian bison - the world's largest bovid), dhole (Indian wild dog), barasingha (swamp deer with 12-tined horns), etc.
https://en.wikipedia.org/wiki/Bengal_tiger
https://en.wikipedia.org/wiki/Gaur
https://en.wikipedia.org/wiki/Dhole
https://en.wikipedia.org/wiki/Barasingha
Marble Rocks - sheer marble cliffs on both sides of the Narmada river near Jabalpur (MP). They offer boat rides down that stretch, so you can see the cliffs from up close. Seen it.
https://en.wikipedia.org/wiki/Marble_Rocks
In South India, less well known places include the "hill stations" (resorts) such as Kodaikanal, Coonoor (5-7000+ feet high, with a cooler climate, and mountain forests and orchards), many less frequented and less crowded beaches, etc. Temples are well known but there are a huge number of them, large and small, many with interesting architecture. Many wildlife sanctuaries in South India too. Seen wild elephants on hikes from the mountains to the plains. Bison too, many times, from nearby. They're huge, but peaceful, unless disturbed. Cape Comorin (Kanya Kumari), the southernmost tip of the Indian peninsula, where the Arabian Sea, Indian Ocean and Bay of Bengal meet. Multi-colored sands there.
Seen some of the above.
The Western Ghats, a long mountain range down the western side of India, right from Mumbai to almost Kankyakumari, including the states of Maharashtra, Goa, Karnataka and Kerala/TamilNadu. Lived in parts of it for some years. It's a biodiversity hotspot, with both deciduous and rain forests.
https://en.wikipedia.org/wiki/Western_Ghats
A concert about India's environment and the Western Ghats, by Chinmaya Dunster and the Celtic Ragas band - A Sense of Wonder:
Go see the wonders of the world. Be in awe.
I would suggest India because it's a microcosm. Go north to the Himalayas and you can feel the majesty. Head to the west to the slums of Mumbai and you will understand poverty. Maybe go learn to meditate out there at a vipassana center. Visit Agra and the goggle at the opulence of the Taj Mahal. Then head to Varanasi and experience the rawness. Maybe you'll even see a miracle or two if you're lucky. Go to Hampi and see giant boulders stacked on top of each other like lego and be bewildered. Stay in a palace just for the hell of it. Take a motorcycle through small villages and be greeted by the children who've never seen anyone so pale or so dark. Sleep in a tent in the deserts of Rajasthan. Visit the holy places and wonder at the peacefulness.
But then again, India isn't for everyone, but it does have everything.