I will try to frame my answer from the perspective of a foreign tourist visiting India to take the best out of this trip and avoid any problems on the way.
Honestly, if you come to India, I would recommend just go to one of these beach destinations like Kerala and Goa. The ideal visiting time is around winter where there is not much humidity and the temps are really good.
Both these spots are really tourist-friendly with people whom you can communicate easily (Obvio they talk english but you can also find people speaking french, spanish, portugese etc to help you out)
The food in both these parts is great, you can also find Beef dishes in Kerala which tbh, you cannot find in the majority of India and many foreigners really crave this meat when coming to India, just so that you know.
The Christmas party in Goa is very famous and hundreds of thousands of tourists visit Goa during that time of the year. It is a very unique experience to celebrate Christmas in 30 degrees Celcius for many Europeans and North Americans.
This is the easiest and effortless route you can take to enjoy and not get yourself tired. Ideal for a vacation.
If you are more into India's culture then ohh boy, prepare to do some trekking and traveling.
I suggest you land in New Delhi rather than Mumbai, go explore Old Delhi. Some posts above have mentioned some popular spots, Chandni Chowk, Qutub Minar, Red Fort and other places which I am sure the place where you stay (your hotel) will be more than happy to help you out with.
Then proceed towards Agra and visit the Taj Mahal and other places near it including Fatehpur Sikri.
This is usually enough for a normal person visiting India for the first time. After this, you can proceed to either Goa or Kerala. Goa is strictly for enjoyment (atleast as a tourist) while Kerala has both culture and good beaches. You can decide likewise.
Some things to note out for in India -
India gets very hot and humid, make sure to drink lots of water and only packaged water or water that you are used to drinking for at least 7-8 days on your arrival. Indians get sick when they go abroad and others when they come to India cause of the different microbiology in different areas.
As much as India gets hot, it also gets cold. Make sure to bring winterwear if you are ever visiting anything that is in the northern half of India during the winter season (November - February). If you arrive (and leave) from Goa or Kerala, you won't need winterwear as they are mostly warm during the winters.
Always make sure you do things that tourists normally do and visit places where tourists normally visit. If at any point you feel like you do not see "white faces" for a while, make sure to return to a place with more tourists or your hotel.
India is safer than it is portrayed but still, it is advised to be at guard regardless.
Shopkeepers like to engage you to buy something and it can get quite hectic. Find a way to deal with them.
Keep talking to your driver/hotel managers/waiters at restaurants, they can let our some unique places to visit and some good food on the menu.
PS - I did not write this whole thing down. Parts of it are copied from a convo I had with someone else visiting India a while ago.