Hi
@amelia88,
I have travelled solo in India quite often and can definitely share some of my experiences. I am Indian, so I realize that it is a little different. Some of my friends from grad school in the US have travelled solo in India, and I can also tell you about their experiences.
Yes, there is a lot of staring and unwanted attention. Mostly, it is just curiosity (especially if you are white and in a non-metropolitan area where white people are rare sights). Generally, things are quite safe, especially if you want to stick to the popular trails and touristy destinations. However, this does not mean that you cannot go to the off-the-beaten-track places - just take a few precautions to be safe, stuff that's just basic common sense in a new and unfamiliar place.
Generally, here's what I would recommend.
1. Know your itinerary before you travel. Book hotel rooms in advance and carry addresses with you in a non-digital format. In case you lose your phone or it is out of charge, you can get to your destination. Choose hotels that are labelled 'for families' on websites like Tripadvisor - that generally means that it is a decent, upmarket place.
2. Leave a copy of your itinerary with a friend back home. Call every day to update them on your whereabouts. Get a phone plan where you can call home or Whatsapp your whereabouts at regular intervals.
3. As far as possible, take pre-paid taxis from the airport (you can find signs at most major airports). To travel within a city or to nearby destinations, have your hotel fix you up with a car and driver. Get the driver's number and the car's number and text it to your friend back home. This is something Indian women travelling alone do all the time.
4. During the day time, most popular destinations should be quite safe. Keep yourself hydrated (with bottled water), wear sunscreen. However, except for big cities, I would not advise venturing out at night (after 8 PM). You may if you have your car and a driver you trust, but most small cities shut down at night, so that night time adventure might not be worth it. Also, driving late at night might not be very safe because some drivers are especially rash at night, when the traffic is less.
5. If you are going off the beaten path, to smaller cities or forests, great! I hope you enjoy it. That is the India I love, and I hope you see. The only things you need to remember is, it is like going to an unfamiliar place in your own home country. The local customs are different, the people have different values etc. Learn about it if you can, respect them. Many people are very hospitable, so chances are you may really enjoy your visit. However, just in general, please do not stay out later than there are women on the roads (that's a really good sign to get a sense for how safe a place is for women. Are there women on the roads?).
6. A lot of people ask about dress codes. Wear what you are comfortable in, but try not to show too much skin, especially in religious places. A friend of mine from the US did something brilliant: she came to India with an empty suitcase, and on her first day here, bought a lot of loose, flowy salwar-kurtas and harem pants. She loved them and she fit right in!
7. If you like to run, try to find a park or a race course in the city you are in. A google search with <name of city + running> usually tells where people in the city run.
This is all I can remember for now. I will add more points as I remember them.
I reiterate this, mostly you are safe. India is a lovely country with so much to see. I hope you have a lovely visit!